A Machian Model of Dark Energy

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Dark Energy Density in Brane World

Λ (Λ < 0) and M are respectively the bulk cosmological constant and funM3 damental energy scale of ﬁve-dimensional gravity. According to the assumption, the metric on the brane world can be written as follows (here ﬁve-dimensional suﬃces are denoted by capital Latin and the four-dimensional suﬃces by the Greek ones), ds2 = e2A(y) gµν dxµ dxν − dy 2 , where gµν is the metric on the brane and gµν = diag 1, − e2 Here √
2
energy density times the radius of the extra dimension. In supersymmetric grand uniﬁed theories (GUT), for instance, in supersymmetric SO(10) model, all of the gauge ﬁeld coupling constants can be uniﬁed. To realize the uniﬁcation of gravitation with other gauge ﬁelds, the fundamental energy scale of ﬁve-dimensional gravity should be the same as the supersymmetric GUT energy scale. When we select the supersymmetric GUT energy scale MG as the fundamental energy scale of ﬁve-dimensional gravity, simultaneously the radius of the AdS5 space-time is admitted by the astronomical observations, the tiny but nonzero four-dimensional cosmological constant can be acquired, which is slightly smaller than the value given by modern astronomical observations.[3, 4] The possible reasons leading to this smallness are also discussed at the end of this paper.

小学上册第十一次英语第三单元期末试卷(含答案)

小学上册英语第三单元期末试卷(含答案)英语试题一、综合题(本题有100小题，每小题1分，共100分.每小题不选、错误，均不给分)1.My aunt has a farm with many ______ (动物).2.The ______ (温室效应) can impact plant habitats.3. A ____(green infrastructure) integrates nature into urban planning.4.I dream of creating a toy that promotes ________ (名词) and kindness.5.The _______ of a pendulum can be affected by its mass.6.The ______ teaches us about modern technology.7.The chemical formula for glucose is __________.8.Cherry _______ are red and delicious to eat.9.The capital of Bonaire is __________.10.The _______ can be a source of food and shelter.11.The cat is very _______ (可爱) and loves to play.12.I want to ________ (innovate) solutions.13.What do we call the outer layer of the Earth?A. CoreB. MantleC. CrustD. Atmosphere答案:C14.Which word means "to look at something closely"?A. StareB. GlanceC. PeekD. Gaze答案: D15.I have a pet ______ (fish).16.The puppy is very ______ (playful).17. A base can neutralize an _______.18.An oxidizing agent is a substance that can accept _____.19.The chemical formula for lithium carbonate is _____.20.I have a toy ________ that can soar through the air.21.What is the name of the famous American singer known for "Like a Prayer"?A. MadonnaB. Britney SpearsC. Lady GagaD. Janet Jackson答案:A22.We have a ______ (愉快的) celebration for achievements.23.My aunt enjoys giving ____ (advice) to others.24.What is the name of the famous English playwright?A. Charles DickensB. William ShakespeareC. George OrwellD. Jane Austen 答案: B25.Read and choose.(看图标号。

Bright High z SnIa∶ A Challenge for LCDM？

w(z)
w0
w1
z 1
z
erroneous 0m
0.22
Sahni, Shafieloo, Starobinsky, PRD 2ous 0m
0.32
Binned Normalized Difference Statistics (BND)
• It is directly applicable on the distance moduli data.
crossing less than or equal to the redshift of crossing in the actual case.
Results
• Models: Phantom Divide Line (PDL) Lambda Cold Dark Matter (LCDM)
• Data: Gold 2006 (182 SnIa) Union 2008 (307 SnIa)
LCDM
Summary:
• According to the BND statistic, Gold06 and Union08 datasets have probability 2.2% and 5.3% to have emerged in the context of LCDM cosmology.
Union08 Data LCDM PDL
Gold data (2006)
LCDM 2.2% Consistency
PDL 32.1% Consistency
Union data (2008)
LCDM 5.3% Consistency
PDL Consistent
Consistency at low redshifts

暗能量与反弹宇宙学中若干问题

(II) Early Universe Application: Bouncing Scenario Introduction to Standard Big-Bang Theory and Inflation; Bouncing Scenario; Calculation on perturbation and signatures on observations; Other properties of bouncing scenario
(IV)Summary
（I） Topics on Dark Energy
DARK ENERGY: A MYSTERIOUS FORCE DRIVING THE ACCELERATION OF THE UNIVERSE
Einstein Equation:
Characteristics of DE: negative pressure, non-clustering…
2.Double-field Quintom model
2.Single simple component
For multi-components:
3.Single scalar field model with Higher Derivatives
3.Minimally coupling to Gravity 4.Non-scalar models (such as spinor, vector, etc)
Candidates of Dark Energy:
I. Cosmological Constant: w=-1;
II. Quintessence -1<w<1;
III. Phantom
w<-1;

Two-field Models of Dark Energy with Equation of State Across -1

The Quintom model considered in refs.[8] and [13] does not include the interaction between the two scalars and is not the most general one. In this paper, we revisit this type of two-ﬁeld Quintom model by introducing a interaction term. We will study in detail the cosmological evolution of this model. In ref.[13] it has been shown that in the two-ﬁeld Quintom model the scaling solution dominated by the Phantom ﬁeld will be a latetime attractor in the absence of the interactions. In this paper by a explicit calculation we will show the interactions do not aﬀect the Phantom-domination attractor behavior. In addition our studies also show that this class of models will provide some interesting possibilities of the evolution of the equation of state which have not been considered in refs.[8] and [13]. Furthermore we will propose in this paper a two-ﬁeld Quintom model with a scalar and a fermion which speciﬁcally we take to be the neutrinos and study its evolution of the equation of state. This paper is organized as follows: in section II we study in detail the model with one Quintessence and one Phantom; in section III we present our model of Quintom with a Phantom and neutrinos; section IV is our conclusion and discussions.

Possible Effects of Dark Energy on the Detection of Dark Matter Particles

a r X i v :h e p -p h /0503120v 1 14 M a r 2005Possible Eﬀects of Dark Energy on the Detection of Dark MatterParticlesPeihong Gu,1Xiao-Jun Bi,2Zhi-Hai Lin,1and Xinmin Zhang 11Institute of High Energy Physics,Chinese Academy of Sciences,P.O.Box 918-4,Beijing 100049,P.R.China2Key laboratory of particle astrophysics,Institute of High Energy Physics,Chinese Academy of Sciences,P.O.Box 918-3,Beijing 100049,P.R.China (Dated:February 2,2008)Abstract We study in this paper the possible inﬂuence of the dark energy on the detection of the dark matter particles.In models of dark energy described by a dynamical scalar ﬁeld such as the Quintessence,its interaction with the dark matter will cause the dark matter particles such as the neutralino vary as a function of space and time.Given a speciﬁc model of the Quintessence and its interaction in this paper we calculate numerically the corrections to the neutralino masses and the induced spectrum of the neutrinos from the annihilation of the neutralinos pairs in the core of the Sun.This study gives rise to a possibility of probing for dark energy in the experiments of detecting the dark matter particles.Recent observational data from supernovae(SN)Ia[1]and cosmic microwave background radiation(CMBR)[2]strongly support for the‘cosmic concordance’model,in which the Universe is spatiallyﬂat with4%baryon matter,23%of cold dark matter(DM)and 73%of dark energy(DE).The baryon matter is well described by the standard model of the particle physics,however the nature of the dark matter and the dark energy remains unknown.There have been many proposals in the literature for the dark matter candidates the-oretically.From the point of view of the particle physics,the leading candidates for cold dark matter are the axion and the neutralino.Various experiments in the search directly or indirectly for these dark matter particles are currently under way.Regarding dark energy,the simplest candidate seems to be a remnant small cosmological constant.However,many physicists are attracted by the idea that dark energy is due to a dynamical component,such as a canonical scalarﬁeld Q,named Quintessence[3].Being a dynamical component,the scalarﬁeld of the dark energy is expected to interact with the other matters[4].There are many discussions on the explicit couplings of quintessence to baryons,dark matter,photons and neutrinos.These interactions if exist will open up the possibilities of probing non-gravitationally for the dark energy.In this paper we consider the possible eﬀects of the dark energy models which interact with the dark matter in the detection of the dark matter particles.Speciﬁcally we will study the inﬂuence of the dark energy on the neutralino masses in the Sun,and then calculate the neutrino spectrum annihilated from the neutralino pairs in the core of the Sun.We start with a coupled system of the interacting dark energy and the dark matter with the Lagrangian generally given byL eff=L DM+Lφ+L int,(1)where L DM and Lφare the free Lagrangian for dark matter and dark energy and the inter-action part is given byL int=−12M2S(φ)S2−gχΛ∂µφ¯ψγµψ−g SΛφ∂µφ∂µS− g isuch as the neutralino to be the dark matter particle and focus on the interactions which aﬀect the dark matter particles via the mass terms.Being a function of the quintessence scalarφthe mass of the dark matter particle will vary during the evolution of the universe.As shown in Refs.[5,6,7]this helps solve the coincidence problem.Furthermore,this type of interactions will aﬀect the cosmic structure formation[8],and the power spectrum of CMB[9].In this paper we will present a new possible eﬀect of the interacting dark energy with the dark matter in the detection of the dark matter particles.There are in general two diﬀerent ways,direct and indirect,in the detections of the dark matter particles.The direct detection records the recoil energy of the detector nuclei when the dark matter particles scatter oﬀthem as they pass through the Earth and interact with the matter.The indirect detection observes the annihilation products by the dark matter particles.Obviously the expected detection rates depend on the mass of the dark matter particles.In the presence of the interaction the mass of the dark matter particle will vary as a function of time and also space,and consequently the dark energy will inﬂuence the detection.To determine the mass of neutralino as a function of space we need to know the value of the dark energy scalarﬁeld as a function of space.Taking into account the back reaction of the interaction between the dark matter and the dark energy the eﬀective potential of the dark energy scalar as a function of the energy density of the cold dark matterρχ(φ)is given byV eff=ρχ(φ)+V(φ).(3) For diﬀerent dark matter densities the values of dark energy scalarﬁeld are expected to be diﬀerent,and consequently the mass of dark matter particles will also be diﬀerent.For example,the mass of the dark matter particle in the center of the Milky Way could be diﬀerent from that in the halo near the solar system.Therefore,the gamma ray spectrum, or the synchrotron radiation spectrum,from the galactic center could be diﬀerent from that in the nearby halo.Especially for the neutralino dark matter particle its mass measured at the future linear collider(LC)or the large hadron collider(LHC)on the Earth may be diﬀerent from that measured in other places in the Milky Way,such as in the galactic center.Similarly,the spectrum of the dark matter radiation in the Milky Way might also be diﬀerent from other galaxies in the local group.In the following we will consider a speciﬁc model of the Quintessence and its interaction with the dark matter particle,the neutralino,and then study its eﬀects on the indirect detection via the process of the neutralinos annihilation into neutrinos.The dark energy potential which we take isV(φ)=V0eβφ/m p,(4) and the interaction between the dark energy and the dark matter particle are given byMχ(φ)=Mχ0 1+λχφ(y q¯Q L Hq R).(6)m pThe parameterλB above characterizing the strength of this type of interaction will be shown below to be strongly constrained.However,since the baryon density inside the Sun is much higher than any other matter densities,this interaction in Eq.(6)will be important to our study in this paper as well as that on the neutrino oscillations[14,17,18].The Eq.(5)shows that the mass of the dark matter particles varies during the evolution of the Universe.At the present time the mass of the neutralino dark matter particle is given by Eq.(5)with the scalarﬁeldφevaluated at the present timeφ0.This type of physics associated with the mass varying dark matter particles have been proposed and studied in the literature[6,9,19],but in these studies the masses of the dark matter particle are constant in space.In this paper we consider the case that neutralino masses vary as afunction of space,for instance the neutralino mass in the Sun diﬀers from that evaluated on the cosmological scale.The eﬀective potential of the dark energy scalar at the inner of the Sun or the Earth is given byV eff =ρB (φ)+ρχ(φ)+V (φ),(7)where ρB (φ)is the mass density of the baryon matter and ρχ(φ)=n χM χ(φ).Here it’s straightforward to obtain ρB (φ)=ρB 0−λB ρB 0φdφφ=φmin=0.(8)The contributions to the equation above from the dark matter and baryon are proportional to λB ρB and λχρχrespectively.Sincethe ρχis about 15orders of magnitude smaller than ρB in the core of the Sun [20],the inﬂuence of the dark matter on the eﬀective potential of the dark energy scalar can be safely ignored ifλB ≫λχρχβln λB ρBM cos χ=1+λχβV 0m p .(11)In Eq.(11)φ0is the cosmological value of the scalar ﬁeld at the present time.To satisfy the cosmological observations on the dark energy our numerical results show that φ0=−0.51m p ,V 0=4.2×10−47GeV 4and β=1and λχ=0.1which we have mentioned above.10-510-410-310-210-1100200300400500600700800900E µ(GeV)ΦµM χ=170GeV M χ=1TeVFIG.1:Spectra of the muons induced by the neutrinos from the annihilation of the neutralino dark matter particles in the core of the Sun with m χ=1TeV and in the cosmological scale with m χ=170GeV.The spectra are normalized at 10GeV and calculated by using the DarkSUSY package [23].The baryon energy density of the Sun ρ⊙B is about 2.5g/cm 3.However due to thelogarithm in Eq.(10),the eﬀect on the dark matter mass is insensitive to the baryon mass density ρB .For example,the baryon density in the Sun ρ⊙B is about a quarter of that inthe Earth,which causes that M ⊙χis about 2%smaller than the value at the Earth in ournumerical calculation for λB =10−9.The parameter λB is constrained by the tests on the gravitational inverse square law [21]and the tests on the equivalence principle [22]to be λB <∼O (10−2).Here we point out that the presence of the interaction of the dark energy with the baryon in Eq.(6)makes the baryon mass density also varyδρBρB =−λB βV 0.(12)If taking ρB (φmin )to be the baryon density in the Earth (which is similar to the baryon density of the Sun),δρB (φmin )indicates the correction of the dark energy to baryon mass in the Earth.The proton mass has been measured very precisely on the Earth with an error of 10−8.If we take as an example that δρB /ρB <10−8we obtain an upper limit on λB ,λB <10−9,which we use in the numerical calculation.Now we have φmin ≃49m p and consequently M ⊙χ/M cos χ≃6.In Fig.1we plot the muonspectra induced by the neutrino from the dark matter annihilation in the center of the Sun and in the cosmological scale.We choose the dark matter mass in the Sun to be1TeV, while the dark matter mass in the cosmological scale is about1TeV/6=170GeV.From the ﬁgure one can see clearly the diﬀerence in the neutrino spectra.On the cosmological scale the dark energy scalar is homogeneously distributed,however in this case it is inhomogeneous,which gives rise to energy densityρφin the Sun.From Eqs.(4)and(10)we haveρφρB =λB[4]See,for example,X.Zhang,Plenary talk at12th International Conference on Supersymmetryand Uniﬁcation of Fundamental Interactions(SUSY04),Tsukuba,Japan,17-23Jun2004, hep-ph/0410292,and references therein.[5] elli,M.Pietroni,and A.Riotto,Phys.Lett.B571,115(2003).[6]U.Franca and R.Rosenfeld,Phys.Rev.D69,063517(2004).[7]X.J.Bi,B.Feng,H.Li,and X.Zhang,hep-ph/0412002.[8]Adi Nusser,S.S.Gubser,and P.J.E.Peebles,astro-ph/0412586.[9]M.B.Hoﬀman,astro-ph/0307350.[10]P.Q.Hung,hep-ph/0010126.This paper is on the interaction between the quintessence andthe sterile neutrinos.[11]P.Gu,X.Wang,and X.Zhang,Phys.Rev.D68,087301(2003).[12]R.Fardon,A.E.Nelson,and N.Weiner,astro-ph/0309800.[13]P.Q.Hung and H.Pas,astro-ph/0311131.[14] D.B.Kaplan,A.E.Nelson,and N.Weiner,Phys.Rev.Lett.93,091801(2004).[15]R.D.Peccei,Phys.Rev.D71,023527(2005);Nucl.Phys.Proc.Suppl.137,277(2004).[16]X.Zhang,hep-ph/0410292;H.Li,Z.Dai,and X.Zhang,hep-ph/0411228.[17] E.I.Guendelman and A.B.Kaganovich,hep-th/0411188.[18]V.Barger,P.Huber,and D.Marfatia,hep-ph/0502196.[19]G.W.Anderson and S.M.Carroll,astro-ph/9711288;G.R.Farrar and P.J.E.Peebles,Astro-phys.J.604,1(2004).[20]G.Bertone,D.Hooper,and J.Silk,Phys.Rept.405,279(2005).[21] E.G.Adelberger,B.R.Heckel,and A.E.Nelson,Annu.Rev.Nucl.Part.Sci.53,77(2003).[22]Y.Su et.al.,Phys.Rev.D50,3614(1994);G.L.Smith et.al.,Phys.Rev.D61,022001(2000).[23]P.Gondolo et.al.,JCAP0407,008(2004).。

Supernova Acceleration Probe Studying Dark Energy with Type Ia Supernovae

a r X i v :a s t r o -p h /0507459v 1 19 J u l 2005Supernova Acceleration Probe:Studying Dark Energy withType Ia SupernovaeA White Paper to the Dark Energy Task ForceJ.Albert 1,G.Aldering 2,S.Allam 3,W.Althouse 4,R.Amanullah 5,J.Annis 3,P.Astier 6,M.Aumeunier 7,8,S.Bailey 2,C.Baltay 9,E.Barrelet 6,S.Basa 8,C.Bebek 2,L.Bergstr¨o m 5,G.Bernstein 10,M.Bester 11,B.Besuner 11,B.Bigelow 12,R.Blandford 4,R.Bohlin 12,A.Bonissent 7,C.Bower 13,M.Brown 12,M.Campbell 12,W.Carithers 2,D.Cole 14,mins 2,W.Craig 4,T.Davis 15,2,K.Dawson 2,C.Day 2,M.DeHarveng 8,F.DeJongh 3,S.Deustua 16,H.Diehl 3,T.Dobson 11,S.Dodelson 3,A.Ealet 7,8,R.Ellis 1,W.Emmet 9,D.Figer 12,D.Fouchez 7,M.Frerking 14,J.Frieman 3,A.Fruchter 12,D.Gerdes 12,L.Gladney 10,G.Goldhaber 11,A.Goobar 5,D.Groom 2,H.Heetderks 11,M.Hoﬀ2,S.Holland 2,M.Huﬀer 4,L.Hui 3,D.Huterer 17,B.Jain 10,P.Jelinsky 11,C.Juramy 6,A.Karcher 2,S.Kent 3,S.Kahn 4,A.Kim 2,W.Kolbe 2,B.Krieger 2,G.Kushner 2,N.Kuznetsova 2,fever 2,moureux 2,mpton 11,O.Le F`e vre 8,V.Lebrun 8,M.Levi 2∗,P.Limon 3,H.Lin 3,E.Linder 2,S.Loken 2,W.Lorenzon 12,R.Malina 8,L.Marian 10,J.Marriner 3,P.Marshall 4,R.Massey 18,A.Mazure 8,B.McGinnis 2,T.McKay 12,S.McKee 12,R.Miquel 2,B.Mobasher 12,N.Morgan 9,E.M¨o rtsell 5,N.Mostek 13,S.Mufson 13,J.Musser 13,R.Nakajima 10,P.Nugent 2,H.Olus .eyi 2,R.Pain 6,N.Palaio 2,D.Pankow 11,J.Peoples 3,S.Perlmutter 2†,D.Peterson 2,E.Prieto 8,D.Rabinowitz 9,A.Refregier 19,J.Rhodes 1,14,N.Roe 2,D.Rusin 10,V.Scarpine 3,M.Schubnell 12,M.Seiﬀert 14,M.Sholl 11,H.Shukla 11,G.Smadja 20,R.M.Smith 1,G.Smoot 11,J.Snyder 9,A.Spadafora 2,F.Stabenau 10,A.Stebbins 3,C.Stoughton 3,A.Szymkowiak 9,G.Tarl´e 12,K.Taylor 1,A.Tilquin 7,A.Tomasch 12,D.Tucker 3,D.Vincent 6,H.von der Lippe 2,J-P.Walder 2,G.Wang 2,A.Weinstein 1,W.Wester 3,M.White 11saul@ melevi@16AmericanAstronomical Society 17Universityof Chicago18Cambridge University 19CEA,Saclay,France20IPNL,CNRS-IN2P3,Villeurbanne,France ∗Co-PI †PInova distance measurements up to their funda-mental systematic limit;strict requirements on the monitoring of each supernova’s properties leads to the need for a space-based mission.Results from pre-SNAP experiments,which characterize fundamental SN Ia properties,will be used to op-timize the SNAP observing strategy to yield data, which minimize both systematic and statistical uncertainties.With early R&D funding,we have achieved technological readiness and the collabo-ration is poised to begin construction.Pre-JDEM AO R&D support will further reduce technical and cost risk.Speciﬁc details on the SNAP mission can be found in Aldering et al.(2004,2005).1.1.Overview of Goals and TechniquesThe primary goal of the SNAP supernova pro-gram is to provide a dataset which gives tight constraints on parameters which characterize the dark-energy,e.g.w0and w a where w(a)=w0+ w a(1−a).SNAP data can also be used to di-rectly test and discriminate among speciﬁc dark-energy models.We will do so by building the Hub-ble diagram of high-redshift supernovae,the same methodology used in the original discovery of the acceleration of the expansion of the Universe that established the existence of dark energy(Perlmut-ter et al.1998;Garnavich et al.1998;Riess et al. 1998;Perlmutter et al.1999).The SNAP SN Ia program focuses on minimiz-ing the systematicﬂoor of the supernova method through the use of characterized supernovae that can be sorted into subsets based on subtle signa-tures of heterogeneity.Subsets may be deﬁned based on host-galaxy morphology,spectral-feature strength and velocity,early-time behavior,inter alia.Independent cosmological analysis of each subset of“like”supernovae can be compared to give conﬁdence that the results are free from sig-niﬁcant systematics.Conversely,analysis between supernova subsets at the same redshift can iden-tify further systematics controls.While theories of the supernova progenitor and explosion mech-anism can guide the establishment of subset cri-teria,such understanding is not required–only comprehensive measurements are–for robustness of the cosmological results.The level of robustness is tied to the quality of data with which supernovae are distinguished.Statistical mission requirements are fundamentally bound by the systematic limi-tations of the experiment.1.2.Description of the Baseline ProposalSNAP is a2-m space telescope(shown in Fig-ure1)with a0.7square-degree instrumented focal plane imager(shown in Figure2)and a low res-olution R∼100integral-ﬁeld-unit spectrograph (schematic shown in Figure3).Both instruments are sensitive to the0.4–1.7µm wavelength range. The two SNAP deep-surveyﬁelds each subtends 7.5square degrees and each is observed approx-imately every four days over the time-scales of supernova light-curve evolution in each of nine passbands.The passbands have resolution∼4.5 and are logarithmically distributed over the full wavelength range.Targeted spectrographic obser-vations are made of discovered supernovae with exposure times tuned to the sourceﬂux.The magnitude depths for individual scans and co-added images of the SNAP supernovaﬁelds are calculated for eachﬁlter.Table1shows the limit-ing S/N=5AB magnitude for eachﬁlter in the “Deep”supernova survey,for point sources that are not contaminated with cosmic rays.The limit-ing magnitude for any given point is probabilistic, due to the random occurrence of cosmic rays.In a single scan of the deep survey,77%of point sources will have no cosmic-ray contamination in any of the four dithered images while98%will have one or fewer cosmic-contaminated image,only slightly reducing signal-to-noise.2.Precursor ObservationsAny precursor mission that characterizes the fundamental properties of SNe Ia and their ap-plicability as distance indicators is important for optimizing the observing strategy and data anal-ysis of SNAP.Low-redshift surveys provide high signal-to-noise,comprehensive observations of well-charac-terized SNe Ia and could provide speciﬁc require-ments for the observation of light-curve or spec-troscopic features linked to SN Ia heterogeneity and homogeneity.Heterogeneous features provide a handle to probe the systematic limitations of our distance indicator and form the criteria by which “like”supernova subsets are deﬁned.Conversely, current distance measurements to supernovae may be found not to be optimal;a diﬀerent mix of ob-Table1The SNAP AB magnitude survey depth for a point source S/N=5.a Filterλeff(˚A)∆λ(˚A)Deep Survey(AB mag)Wide-ﬁeld Survey Panoramic 14400100027.930.628.326.7 25060115027.930.628.326.8 35819132227.830.528.226.8 46691152027.830.428.126.8 57695174927.830.428.126.8 68849201127.730.328.026.7 710177231327.530.127.826.6 811704266027.530.127.826.6 913459305927.430.027.726.51.5 degreeFig.2.—The SNAP focal plane working concept. The two-axis symmetry of the imagerﬁlters allows any90◦rotation to scan aﬁxed strip of the sky and measure all objects in all nineﬁlter types.The im-ager covers0.7square degrees.Underlying theﬁl-ters,there are362k x2k HgCdTe NIR devices and 363.5k x3.5k CCDs on a140K passively-cooled focal plane.The six CCDﬁlter types and three NIRﬁlters are arranged so that vertical or hori-zontal scans of the array through an observation ﬁeld will measure all objects in allﬁlters.The false colors indicateﬁlters with the same bandpass.The central rectangle and solid circle are the spectro-graph body and its light access port,respectively. The spectrum of a supernova is taken by placing the star in the spectrograph port by steering the satellite.The four small,isolated squares are the star guider CCDs.The inner and outer radii are 129and284mm,respectively.Fig. 3.—A schematic spectrograph optical de-sign.The beam is going out from the slicer(on the bottom right)to a prism disperser back faced coated by a dichroic.The visible light(blue path) is reﬂected and the IR light(in red)continue to a second prism used to reach the required spectral dispersion.The two beams are therefore focused on two detectors.The dimensions of the spectro-graph are approximately400×80×100mm.See Ealet et al.(2003)for more details.dark-energy properties,especially the time vari-ation of the equation of state.3.1.Sources of Systematic UncertaintyHigh-redshift supernova searches have been proceeding since the late1980’s(Norgaard-Nielsen et al.1989;Couch et al.1989;Perlmutter et al. 1995,1997,1998,1999;Schmidt et al.1998;Riess et al.1998;Tonry et al.2003;Knop et al.2003; Riess et al.2004).Particularly since the discov-ery of the accelerating expansion of the Universe, the high-redshift supernova methodology for mea-suring cosmological parameters has been critically scrutinized for sources of systematic uncertainty. Below(and summarized in Table2)is a lists of these sources where we highlight in bold the fea-tures speciﬁc to SNAP that allow systematic con-trol.Generically,the need for high signal-to-noise observations over a broad wavelength range for 0.1<z<1.7supernovae,as well as the truncation of ground-observatory light curves of high-redshift supernova at high-Galactic latitude,point to the necessity of a space mission.Table2SNAP Control of Sources of Astrophysical Systematic Uncertainty Systematic Control3.1.1.Evolution of the Supernova Sample as aFunction of RedshiftThe luminosity function of supernovae may evolve as a function of redshift resulting in cor-responding biases in distance-modulus determina-tions(Perlmutter et al.1995).Although like su-pernovae have the same redshift-independent lu-minosity,their relative rate of occurrence may evolve in redshift.SNAP addresses this problem by identifying subsets of supernovae“identical”in luminosity and color,applying the dark-energy analysis to each,and optimally combining the subset re-sults intoﬁnal cosmology measurements.We exploit the fact that supernovae cannot change their brightness in one measured wavelength range without aﬀecting brightness somewhere else in the spectral time series—an eﬀect that is well-captured by expanding atmosphere computer models(e.g.H¨oﬂich&Khokhlov1996;Lentz et al. 2000;H¨oﬂich et al.2003).Well-characterized su-pernovae can be sorted into subsets based on sub-tle signatures of heterogeneity.Subsets may be de-ﬁned based on host-galaxy morphology,spectral-feature strength and velocity,early-time behavior, and light-curve characteristics.There are a number of supernova parameters that are observed to exhibit heterogeneity beyond the single-parameter description.The following features need to be monitored to check for sys-tematic bias in supernova distances.Premaximum spectral screening:Broad-light-curve supernovae can be distinguished by hav-ing either peculiar(e.g.SN1991T)or“normal”(e.g.SNe1999ee and2000E)pre-maximum spec-tra.In addition,there are extremely peculiar sin-gleton events technically classiﬁed as SNe Ia which bear little observational resemblance to their more standard counterparts.These include SN2000cx (Li et al.2001;Candia et al.2003),SN2001ay (Phillips et al.2003),SN2002cx(Li et al.2003), and SN2002ic(Deng et al.2004).These extreme events are easily identiﬁed through their premax-imum peculiar spectra,Hydrogen emission,and high expansion velocities.Spectral-feature velocities:The diversity in the velocity of the6100˚A SiII feature atﬁxed epochs has been noted(Branch&van den Bergh1993; Hatano et al.2000).Garavini et al.(2004)and Benetti et al.(2004)have examined the velocity as a function of supernova phase andﬁnd that large subset of objects tightly cluster within a103 km s−1range for any given epoch.A smaller sub-set with much higher velocity dispersion can be partially distinguished through accurate measure-ments of the SiII feature velocity.Spectral-feature velocity evolution:Benetti et al.(2004)ﬁnd that supernovae cluster when parameterized by the rate of change of the SiII feature velocity˙v and luminosity.Resolution of the velocity gradients requires measurement of˙v to a few km s−1d−1from spectra between peak and40SN-frame days after peak brightness.Spectral-line-ratio:At t<−10,the ratio of line depths of SiII(λ6150˚A)and SiII(λ5800˚A),R(SiII) (Nugent et al.1995),has a range greater than0.1. The subpopulation of supernovae with high veloc-ity gradients also have distinct R(SiII)evolution; they sharply decrease until t=−5andﬂatten out whereas other supernovae show no evolution for the same time range(Benetti et al.2004).Light-curve evolution:There are a series of supernovae that exhibit systematic deviations in light-curve shape and color(e.g.Hamuy et al. 1996;Richmond et al.1995;Krisciunas et al.2003; Pignata et al.2004).The ranges displayed in the optical light curves can be summarized as follows: 1mag10days before maximum and0.2mag5 days before maximum,0.1mag20-30days after maximum,and0.2-0.3mag60days after maxi-mum.Color:There is evidence that color is a second parameter correlated with peak magnitude(Tripp 1998;Saha et al.1999;Tripp&Branch1999;Par-odi et al.2000).Dust extinction and intrinsic su-pernova color can be distinguished as supernovae get brighter in I as V−I color becomes red,the opposite eﬀect from dust.Color measurements whose propagated uncertainties in the extinction correction are less than the intrinsic B peak mag-nitude dispersion correspond to B−V measured to0.07mag and V−I to0.5mag.Polarization:Normal-and broad-light-curve supernovae have demonstrated varying degrees of polarization(Howell et al.2001).Detection of po-larization is extremely diﬃcult for all but the near-est supernovae and is unrealistic to require in any cosmological survey.Spectroscopy may then serve as a proxy for polarization measurements through their correlation with high and quickly evolving SiII velocities.The SNAP instrumentation suite is de-signed to provide the data necessary for the subclassiﬁcation process.SNAP will ob-tain broadband photometry over the full supernova-frame optical region,withﬁne light-curve sampling tuned to natural su-pernova time scales.The SNAP spectro-graph also covers the supernova-frame op-tical region with resolution tuned to the widths of the supernova features.We expect that any residual luminosity and color biases will be smaller than the dispersion observed in the local supernova sample since this represents heterogeneous and diverse supernova-progenitor environments(Branch2001).This assumption will be tested by intensive precur-sor supernova-characterization experiments and SNAP itself.3.1.2.K-correctionA given observing passband is sensitive to dif-ferent supernova-rest-frame spectral regions.K-corrections are used to put these diﬀering photom-etry measurements onto a consistent rest-frame passband(Kim,Goobar,&Perlmutter1996;Nu-gent,Kim,&Perlmutter2002).The SNAP ﬁlter-set number,density,and shapes are tuned to give<0.02mag dispersion for the full catalog of currently available SN Ia spectra(Davis et al.2004).The situation will improve further for the conﬁned analysis of supernova subsamples with the expanded spectral library provided by on-going surveys and SNAP itself.3.1.3.Galactic ExtinctionExtinction maps of our own Galaxy are uncer-tain by∼1–10%depending on direction(Schlegel, Finkbeiner,&Davis1998).Supernovaﬁelds can be chosen toward the low-extinction Galactic caps where uncertainty can then be controlled to< 0.5%in brightness.These levels of uncertainty have negligible eﬀect on the measurement of w0 and w a(Kim&Miquel2005).Spitzer obser-vations will allow an improved mapping between color excesses(e.g.of Galactic halo subdwarfs in the SNAPﬁeld)and Galactic extinction by dust (Lockman&Condon2005).3.1.4.Cross-Passband CalibrationUncertainties in calibration are one of the im-portant limiting factors in probing the dark energy with supernovae.Distance measurements funda-mentally rely on the comparison ofﬂuxes in dif-ferent passbands:for determining the relative dis-tances of supernovae at diﬀerent redshifts and for color measurements for determining the dust ab-sorption of a single supernova.The relationship between passband calibration and w0and w a is strongly dependent on the speciﬁcs of the cross-band correlations.Simula-tion studies(Kim&Miquel2005)demonstrate the strict fundamental limits in the measurement of dark-energy parameters due to uncorrelated cross-band calibration uncertainty.Signiﬁcantly larger correlated uncertainties can be tolerated(Kim et al.2004).These studies provide requirements for the SNAP calibration program.3.1.5.Extinction by Host-Galaxy DustExtinction from host-galaxy dust can signiﬁ-cantly reduce the observed brightness of a dis-covered supernova.SNAP’s9-band photom-etry will identify the properties of the ob-scuring dust and gas,and thus the amount of extinction suﬀered by individual super-novae.Incoherent scatter in dust properties yields no bias but increased statistical uncertainty in the dark-energy parameters(Linder&Miquel 2004).Systematic host-galaxy extinction uncer-tainty can be introduced if an incorrect mean dust-extinction law is used in the analysis.This can be minimized by distinguishing and exclud-ing highly-extincted supernovae from the analysis.To give a quantitative example,sup-pose that the Cardelli et al.(1989)model ac-curately describes host-galaxy extinction and an R V=3.1dust is used in the analysis and the 4400–5900˚A rest-frame color is used to determine A V.We calculate that if drift in the mean of the true dust extinction models is constrained to have 2.4<R V<4.4,the vast majority of supernova which have A B<0.1(Hatano,Branch,&Deaton 1998)would have distance-modulus bias of<0.02 mag.3.1.6.Gravitational LensingInhomogeneities along the supernova line of sight can gravitationally magnify or demagnify the supernovaﬂux and shift the mode of the super-nova magnitude distribution by<∼3%dependingon redshift(Holz&Linder2005).Gravitational lensing magniﬁcation is achromatic and unbiased inﬂux so eﬀectively contributes a statistical uncer-tainty that can be reduced below1%in distance if large numbers(>∼70)of supernovae are ob-tained per0.1redshift bin.The eﬀectiveﬂux dispersion induced by lensing goes asσ=0.088z (Holz&Linder2005).3.1.7.Non-SN Ia ContaminationOther supernova types are on average fainter than SNe Ia and their contamination could bias their Hubble diagram(Perlmutter et al.1999). Observed supernovae must be positively identi-ﬁed as SN Ia.As some Type Ib and Ic super-novae have spectra and brightnesses that other-wise mimic those of SNe Ia(Filippenko1997),a spectrum covering the deﬁning rest frame Si II6150˚A feature and SII features for ev-ery supernova at maximum will provide a pure sample.3.1.8.Malmquist BiasAﬂux-limited sample preferentially detects the intrinsically brighter members of any population of sources.The amount of magnitude bias de-pends on details of the search but can reach the level of the intrinsic magnitude dispersion of a standard candle(Teerikorpi1997).Directly cor-recting this bias would rely on knowledge of the SN Ia luminosity function,which may change with lookback time.A detection threshold fainter than peak by at leastﬁve times the intrin-sic SN Ia luminosity dispersion ensures sam-ple completeness with respect to intrinsic super-nova brightness,eliminating this bias(Kim et al. 2004).3.1.9.Extinction by Hypothetical Gray DustA systematics-limited experiment must ac-count for speculative but reasonable sources of uncertainty such as gray dust.As opposed to normal dust,gray dust is postulated to pro-duce wavelength-independent absorption in opti-cal bands(Aguirre1999;Aguirre&Haiman2000). Although models for gray-dust grains dim blue and red optical light equally,near-infrared light (∼1-2µm)is less aﬀected.Cross-wavelength calibrated spectra extending to wavelength regions where“gray”dust is no longer gray will detect and correct for the hypotheticallarge-grain dust.Numerous observations already severely limit the cosmological eﬀects of such a component(Goobar,Bergstr¨o m,&M¨o rtsell 2002).3.2.Statistical Supernova SampleThe statistical supernova sample appropriate for experiments with the presence of systematic uncertainty has been considered in the Fisher-matrix analysis of Linder&Huterer(2003)and validated with our independent Monte Carlo anal-ysis.They examined the measurement precision of dark-energy parameters as a function of red-shift depth considering2000SNe Ia measured in the range0.1≤z≤z max,along with300low-redshift SNe Ia from the Nearby Supernova Fac-tory(Aldering et al.2002).They concluded that a SN Ia sample extending to redshifts of z∼1.7 is crucial for realistic experiments in which some systematic uncertainties remain after all statisti-cal corrections are applied.Ignoring systematic uncertainties can lead to claims that are too opti-mistic.Statistically,∼2000SNe Ia well-characterized “Branch-normal”supernovae provide systematic-uncertainty limited measurements of the dark-energy parameter w a.These represent the cream, z<1.7supernovae of the∼10000total and ∼4000well-characterized SNAP SNe Ia,that can provide robust cosmological measurements(e.g. non-peculiar,low-extinction).This large sample is necessary to allow model-independent checks for any residual systematics or reﬁned standardization parameters,since the sample will be subdivided in a multidimensional parameter space of redshift, light curve-width,host properties,etc.The large number of lower signal-to-noise light curves from supernovae at z>1.7will provide an extended redshift bin in which to check for consistency with the core sample.We require a statistical measurement uncer-tainty for the peak magnitude corrected for ex-tinction and shape inhomogeneity roughly equal to the current intrinsic magnitude dispersion of supernovae,∼0.15mag.4.Quantiﬁcation of Dark EnergyExpected measurement precisions of the dark-energy parameters w0and w′(=w a/2)for the SNAP supernova program are summarized in Ta-ble3and shown in Figure4.Since SNAP is a systematics-limited experiment,any improve-ments in our projection of systematic uncertainty will be directly reﬂected in improvements in our w0–w′measurements.We determine precisions for twoﬁducialﬂat universes withΩM=0.3,one in which the dark energy is attributed to a cosmolog-ical constant and the other to a SUGRA-inspired dark-energy model(Brax&Martin2000).Fig.4.—The68%conﬁdence region in the dark-energy parameters forﬁducial cosmological con-stant(labeled withΛ)and supergravity(labeled with S)universes.The blue solid curves show the results of the supernova simulation and as-sociated systematic-error model,with a Planck prior on the distance to the surface of last scat-tering,and an assumedﬂat universe.We deﬁne w′≡−dw/d ln a|z=1.See Albert et al.(2005)for constraints including the weak lensing half of the mission.If the universe is taken to be spatiallyﬂat,the SN data(with Planck prior on the distance to the surface of last scattering)determineΩM to 0.01.The present value of the dark energy equa-tion of state is constrained within0.09and the physically crucial dynamical clue of the equation of state time variation is bounded to within0.19. Note that these constraints are systematics lim-ited;much tighter constraints would be obtained if systematics were ignored.Table3also high-Table3SNAP1-σuncertainties in dark-energy parameters,with conservative systematics for the supernova and the shear power-spectrum measurement from a1000sq.deg.one-year weak-lensing survey.Note:These uncertainties are systematics-limited,not statisticslimited.σΩMσΩwσwσw′SNAP SN;w=−10.020.05······SNAP SN+WL;w=−10.010.01······SNAP SN;σΩM=0.03prior;ﬂat;w(z)=w0+2w′(1−a)···0.030.090.31SNAP SN;Planck prior;ﬂat;w(z)=w0+2w′(1−a)···0.010.090.19 SNAP SN+WL;ﬂat;w(z)=w0+2w′(1−a)···0.0050.050.11Fiducial Universe:ﬂat,ΩM=0.3,SUGRA-inspired dark energyNote.—Cosmological and dark-energy parameter precisions for twoﬁducialﬂat universes withΩM=0.3,one in which the dark energy is attributed to a Cosmological Constant and the other to a SUGRA-inspired dark-energy model.The parameter precisions then depend on the choice of data set,priors from other experiments(e.g.Planck measurement of the distance to the surface of last scattering), assumptions on theﬂatness of the universe,and the model for the behavior of w.SNAP is a systematics-limited experiment so any improvements in our projection of systematic uncertainty will be directly reﬂected in improvements in our w0–w′measurements.In this paper we deﬁne w′≡−dw/d ln a|z=1.SNAP can accumulate a wide-ﬁeld weak-lensing survey at a rate of1000sq.deg.per year of observation.lights the signiﬁcant value added by measurements of the shear power spectrum with the complemen-tary SNAP weak-lensing program.The precise,homogeneous,deep supernova data set can alternatively be analyzed in a non-parametric,uncorrelated bin,or eigenmode method(Huterer&Starkman2003;Huterer& Cooray2005).One can also obtain the expansion history a(t)itself,e.g.Linder(2003).5.Project Risks and StrengthsThe proposed experiment is a self-contained su-pernova program which is desensitized to cross-experimental calibration,one of the largest sources of systematic uncertainty.The SNAP instrumen-tation suite provides access to any supernova ob-servable anticipated to be important for reducing uncertainties in supernova distances.The SNAP collaboration is large and diverse, which has allowed for substantial eﬀorts to be sup-ported in science reach,computer framework and simulation,calibration approaches,and photo-detector technology development and testing.Our ongoing R&D eﬀorts have placed us at a point of technological readiness to commence construction of the experiment.The major risk to the SNAP collaboration is that a stretch in the JDEM decision making pro-cess and follow-on project funding will lead to a dissipation of the present eﬀorts as people drift oﬀto other intermediate projects.6.Requisite technology R&DA few areas of the SNAP mission implementa-tion require development to achieveﬂight readi-ness.No new technologies are required,rather particular instances of the technology as chosen by SNAP require some maturation.At present, the SNAP R&D program is primarily funded by the Department of Energy(DOE),with addi-tional support to collaborators from NSF,NASA, CNES,and CNRS/IN2P3for related activities. The SNAP mission architecture has undergone nu-merous studies(GSFC/IMDC,GSFC/ISAL,and JPL/Team-X),has been reviewed several times by external teams of experts at the request of DOE and NSF,and has been extensively presented and discussed at a variety of international conferences.Thus,SNAP is a relatively well-advanced concept, and the internally self-consistent reference model presented here is now ready for more reﬁned opti-mization.R&D has focused on1)SNAP-speciﬁc detector development,both visible and near infrared,2)in-tegralﬁeld unit spectrograph design,3)cold front-end electronics,4)calibration procedures and sup-portingﬂight hardware,5)achievable telescope point stability studies,6)on-board data handling, and7)achievable telemetry rate studies.All of these areas are maturing at a rapid rate and there appear to be no show stoppers for a SNAP JDEM response.Visible detectors:The visible portion of the im-ager is an array of36silicon CCDs with extended red response and improved radiation tolerance. SNAP will materially beneﬁt from an advanced technology based on fully depleted backside illu-minated high resistivity silicon.The development work is DOE funded and is taking place at LBNL and at commercial foundries.We are also devel-oping custom integrated circuits for the electronic readout.NIR detectors:The NIR portion of the imager requires362kx2k format devices.We are evalu-ating HgCdTe devices available from two vendors. Development work funded by DOE is under way to improve the dark current,read noise,and quan-tum eﬃciency.We are also exploring InGaAs as a backup photoactive material.One NIR vendor will provide a cold front-end ASIC for their detec-tors.For the other,we are leveraging the work we have done for the CCDs to provide cold front-end ASICs.Spectrograph:This is a simple two-prism de-sign with no technology challenges except its in-tegralﬁeld unit(IFU).An image-slicer IFU with the requisite size and eﬃciency have been built for ground-based astronomy,and will beﬂown as part of the JWST NIRSPEC.The image slicer R&D is funded by CNES and CNRS/IN2P3.Telescope:This has been studied by the God-dard/ISAL and four prospective space optics sup-pliers.Two industry study contracts are in place to evaluate the design,manufacturability,and testability of the telescope.Studies and vendor discussions have shown that the pointing stability requirements can be met with today’s spacecraft。

你最想和哪一位名人共进晚餐英语作文

你最想和哪一位名人共进晚餐英语作文Who Would I Most Want to Have Dinner With?If I could have dinner with any famous person in the whole world, I would pick Albert Einstein. He was a really smart scientist who came up with some amazing theories about how the universe works. I think it would be so cool to talk to someone like that and learn all about his ideas.I first learned about Albert Einstein in science class when we were studying physics. My teacher told us that he came up with the theory of relativity, which explains how space and time are sort of stretchy and bendy. It's a pretty mindblowing idea when you think about it! The teacher said Einstein realized that the laws of physics are the same for anything moving at a constant speed, no matter how fast that speed is. That's where the name "relativity" comes from.We also learned that Einstein figured out the famous equation E=mc2, which shows that energy and matter are basically two sides of the same coin. Matter can be turned into energy, and energy into matter. That's the principle that lets nuclear power plants work, by splitting atoms apart and capturing the energy released. It's also what makes nuclearbombs so destructive. Just a tiny bit of matter contains a huge amount of pent-up energy when you calculate it using E=mc2.In class, the teacher told us Einstein had really crazy hair that stuck out in all directions. She showed us some funny pictures of him where he was sticking his tongue out and crossing his eyes. I thought it was hilarious that such a brilliant mind could also be such a goofball! It made me realize that even geniuses are just regular people at heart.I'd love to ask Einstein all about how he came up with his revolutionary ideas. What gave him the intuition to re-think the fundamentals that everyone had taken for granted for centuries? Did it start with a blinding insight or was it a long process of step-by-step reasoning? I can't even imagine how someone could look at the world in such a radically new way.It would be so fascinating to pick his brain about other mysteries of the universe that still baffle scientists today. Like what is the true nature of black holes, or of dark matter and dark energy? Could there be other dimensions or parallel universes besides the three spatial dimensions and one time dimension that we know? Could he explain mind-bending concepts like quantum entanglement in a way that a kid could wrap their head around?Beyond just the science itself, I'd really want to know what makes a genius genius tick. What was Einstein like as a kid – was he a prodigy who blazed through childhood or did he seem ordinary until his talents emerged later? How did he develop his incredible powers of creativity, visualization, and analytical reasoning? What drove his insatiable curiosity and willingness to question conventional wisdom? Did he study and work incredibly hard or did insights tend to come in flashes of inspiration?I'd ask Einstein if he had any hobbies or did he pretty much just think about science all the time? If he did have outside interests, what were they? The pictures make him seem like maybe he played an instrument or had an quirky sense of humor. Or did the relentless gears of his mind never stop turning, always pondering the deepest questions of the cosmos?Another thing I'd love to quiz Einstein about is what he thought about the philosophical and spiritual implications of his theories. His famous quote "God does not play dice with the universe" makes it sound like he believed in some higher organizing force or grand design. But at the same time, he also said "I do not believe in a personal God." So I'd ask him toelaborate on his beliefs and whether he felt science and religion were compatible or completely separate realms.It would be really special to get Einstein's perspective on creativity and where brilliant ideas come from. I'm sure he didn't just pull his theories out of thin air – his breakthroughs must have been the product of intuition shaped by years of studying and deep thought. I'd ask him if he had any techniques for fostering the free-flowing mindset that can lead to new insights, like taking long walks or letting his mind wander.Of course I'd probably get tongue-tied and star-struck actually talking to such an iconic genius in the flesh! But hopefully he would be patient with me and share some wisdom about not just physics, but about life, learning, and opening one's eyes to the wonders of the world around us. I have a feeling spending even just one dinner picking Einstein's incredible brain would be a mind-expanding experience I'd never forget.Maybe if I studied hard and never stopped being curious, asking questions and thinking outside the box, a young student like me could grow up to make our own important contributions to human knowledge someday. Sitting across the table from Einstein could very well plant the seeds of inspiration for a futuregeneration of innovators and big thinkers. An evening in the presence of such brilliance could potentially change the course of a young person's life.Even if I didn't go on to become a physicist or make any earth-shattering discoveries, having dinner with Albert Einstein would no doubt leave me in awe of the human mind's ability to reveal and comprehend the deepest realities of our vast, mysterious universe. And hopefully some of his playful sense of humor and childlike wonder would rub off as well! A man who revolutionized our understanding of space and time while still finding joy and laughter in life would make for a truly fascinating dinner companion. It would be a memory to cherish forever –breaking bread with one of history's greatest thinkers.。

科普暗物质支配宇宙英语短文

科普：暗物质支配宇宙（英语短文＋翻译）2009年11月3日星期二Dark Forces Dominate(支配) Universe暗物质支配宇宙The Earth，moon，sun and all visible stars in the sky make up less than one percent of the universe 月亮，太阳和天空上所有的可见星占宇宙的比例不到1％.Almost all the rest is dark matter and dark energ own forces that puzzle astronomers．其余的都是另天文学家迷惑的暗物质,暗能量和未知的力量. Observations in recent years have changed the basic understanding of how the universeevolved（发展进化）and have emphasized（强调）for astronomers how little is known about the majo s andsubstances that shaped our world．最近几年的观察资料已经改变了宇宙如何进化发展发展的基本观点,而且强学家对世界的主要力量和物质发展所知甚少.Astronomers now know that luminous（发光的明亮的）matter-stars．planets and hot gas accounts for out 0.4 percent of the universe．Non luminous components such as black holes and intergalactic gas，up 3.6 percent．The rest is either dark matter, about 23 percent，or dark energy, about 73 percent．天现在知道发光的恒心和热气仅仅占宇宙的0.4％.不发光的黑洞和银河间的气体占宇宙了3.6％.其余的就是暗物质3％,暗能量占73％.Dark matter, sometimes called “cold dark matter,” has been known for some time. Only recently have chers come to understand the pivotal（关键）role it played in the formation of stars．planets and eve le．“We owe our very existence to dark matter,” said physicist Paul Steinhardt and a co-author of a re n dark matter which appeared not long ago in the journal Science．暗物质也就"冷暗的物质",它被人们知有一些时间了.仅仅是最近才有研究人员理解了暗物质在星体中所起的关键作用.我们的生活多亏了暗物质的存在学家Paul Steinhardt 和他的合作者在不久前出版的科学杂志上说.Steinhardt said it is believed that following the Big Bang（宇宙大爆炸），the theoretical beginning of th erse，dark matter caused particles（粒子）to clump together．That set up the gravitation（地心吸力，力）processes that led to the formation of stars and galaxies（星系）．Those stars，in turn，created t c chemicals，such as carbon and iron．that were fundamental to the evolution（进化）of life．Steinh 宇宙被认为是在一次宇宙大爆炸中产生的,在宇宙理论的诞生之处,暗物质时粒子结合在一起.它们在万有引力的作形成星星和星系.这些星系又创造了基本的化学物质.象炭和铁.这些是生命进化的基础.“Dark matter dominated the formation of structure in the early universe．”Steinhardt said．“For the first llion years dark matter contained most of the mass of the universe．You can think of ordinary matter oth of an Ocean of dark matter．The dark matter clumps and the ordinary matter falls into it．That le e formation of the stars and galaxies．”Without dark matter,“there would be virtually no structures in th erse．”暗物质支配着早期宇宙的结构和形式,Steinhardt说.在最初的几十亿年里,暗物质在宇宙中比例很大.你可以通的物质就象是在暗物质的海洋里的气泡.暗物质和普通物质容在一起.这是银河和星系的基础.没有暗物质就没有的结构.The nature of dark matter is unknown．It cannot be seen or detected directly．Astronomers know it is because of its effect on celestial objects than can be seen and measured．自然界的暗物质是不可知的.它看到或直接探测.天文学家知道它们在那儿是因为它们对天上的物体有影响,因此可以被看到和测量.But the most dominating force Of all in the universe is called dark energy．a recently proven power th onomers say is causing the galaxies in the universe to separate at a faster and faster speed．One sc said it is clear now that dark matter and dark energy engaged in a gravitational tug of war that，even dark energy won．大多数的支配宇宙的力量都称为暗能量.物理学家说宇宙中的星系现在以越来越快的速度分物理学家说很显然暗物质和暗能量参加了一场引力的战斗,最终,暗物质获胜.注:翻译的比较粗糙,有的地方可能有错误后不清楚的地方,请大家指正啊!。

最喜欢的科学家爱因斯坦作文英语

最喜欢的科学家爱因斯坦作文英语全文共3篇示例，供读者参考篇1My Favorite Scientist: Albert EinsteinEver since I was a young child, I have been fascinated by science and the natural world around us. From studying planets and stars in our galaxy to learning about the tiny atoms that make up all matter, the wonders of science have captivated my mind and imagination. However, no scientist has inspired me more than the brilliant Albert Einstein.Einstein is arguably the most famous scientist in modern history. His theories revolutionized physics and the way we understand energy, mass, gravity, space and time. He developed the ground-breaking theory of relativity, which fundamentally changed our perception of the universe. Yet what makes Einstein truly remarkable goes far beyond his scientific achievements.First and foremost, Einstein had an incredible thirst for knowledge from a very young age. Born in Germany in 1879, he grew up constantly questioning the world around him. As a child, he devoured science books and performed thought experimentsthat challenged the accepted laws of physics. Einstein's immense curiosity and passion for learning never ceased, even as he became one of the most famous scholars on the planet.His childlike sense of wonder at the mysteries of the universe stayed with Einstein throughout his life. In his famous quote, he poetically remarked, "The most beautiful thing we can experience is the mysterious. It is the source of all true art and science." To Einstein, the journey of intellectual discovery and unraveling the secrets of our reality was a thing of unparalleled beauty.Despite his genius-level intellect, Einstein always maintained a humble demeanor. He believed that "a spirit is manifest in the laws of the universe" and that the role of a scientist is to simply uncover and describe these intrinsic laws, not create them. This perspective helped Einstein avoid arrogance and approach his work with humility.His unassuming nature also led Einstein to live a relatively simple lifestyle, despite his immense fame and success. He owned few personal possessions, wore simple clothes, and focused his energy on contemplating the deepest questions about the fabric of our existence. In many ways, he embodied thearchetype of the "absent-minded professor" who was more interested in intellectual pursuits than material wealth.Perhaps Einstein's most powerful quality was his unrelenting determination and ability to think completely originally. While developing his theory of relativity, Einstein spent years visualizing what would happen if he traveled at the speed of light. This "thought experiment" allowed him to ultimately deduce that the laws of physics are the same for all non-accelerating observers, and that the speed of light is independent of the motion of all observers.These were earth-shattering concepts that overturned centuries of established physics laid out by Newton and others. It took Einstein tremendous courage and conviction to contradict the prevailing beliefs of the scientific community. Years of being dismissed and labeled a "rebel" did not deter him from championing his revolutionary ideas.At the same time, Einstein approached even his most complex theories with a beautiful simplicity and elegant logic. He had the ability to take extraordinarily complex mathematical and scientific concepts and summarize them in strikingly simple maxims. His famous equation E=mc2, which reveals that energyand mass are interchangeable, is a perfect example of expressing an immensely profound insight with straightforward simplicity.Beyond his scientific brilliance, Einstein was also an exceptional writer and public communicator. He had a true gift for articulating abstract theories in ways that captivated audiences of all backgrounds. Despite being consumed by his intellectual endeavors, Einstein made spreading scientific knowledge accessible to all people a core part of his life's mission.Moreover, Einstein applied his genius in physics to weigh in on broader philosophical questions about the universe. He made immense contributions to the scientific understanding of cosmology and the origin of the universe itself. However, Einstein also grappled with the role of God, free will, and the search for meaning in our vast cosmos. His opinions on these existential topics remain endlessly thought-provoking even today.Ultimately though, Einstein will be best remembered not just as a scientific icon, but as a eternally humble, curious, and determined seeker of truth. His pursuit of unraveling the deepest mysteries of our reality has inspired countless young people like myself to follow our intellectual passions fearlessly. With histrademark wild hair, warm human spirit, and unending sense of wonder, Albert Einstein has become the face of genius itself.Whether he was formulating earth-shattering theories or playing his beloved violin, Einstein approached life with joy, humility, and authenticity. He represented the idea that the boundaries of human knowledge are limitless, as long as we maintain open minds and insatiable curiosity. For showing the world the power of pure intellect and imaginative thinking, Albert Einstein will forever be my favorite scientist and hero.篇2My Favorite Scientist: Albert EinsteinWhen I was just a little kid, I remember seeing pictures of this crazy-haired old man sticking his tongue out playfully. At the time, I had no idea who he was or why he was so famous. But as I grew older and began to learn about science and the brilliant minds behind the greatest discoveries and theories, one name kept coming up again and again: Albert Einstein. The more I learned about this remarkable man, the more fascinated I became by both his monumental contributions to physics and his unique way of viewing and experiencing the world aroundhim. Today, Albert Einstein is undoubtedly my favorite scientist of all time.Einstein was born in Germany in 1879, at a time when the field of physics was being revolutionized by new ideas and radical theories. Even from a young age, Einstein displayed a brilliant intellect and an insatiable curiosity about the fundamental laws that govern the universe. He was deeply philosophical, constantly questioning accepted truths and pushing the boundaries of human knowledge. His unique way of thinking allowed him to approach age-old problems from entirely new perspectives.In 1905, when Einstein was just 26 years old, he published four groundbreaking papers that would forever change the course of modern physics. In one of these papers, known as the "Annus Mirabilis Papers," Einstein introduced his Theory of Special Relativity, which completely shattered the conventional understanding of space, time, energy, and matter. This theory postulated that the laws of physics are the same for all observers moving at constant speeds relative to one another, and that the speed of light is constant and independent of the motion of its source. Mind-blowing concepts like time dilation, lengthcontraction, and the equivalence of mass and energy (E=mc^2) formed the backbone of this revolutionary theory.At first, the scientific community was highly skeptical of Einstein's radical ideas. After all, how could our common-sense notions of space and time be so drastically wrong? But as more experiments were conducted to test his predictions, the evidence became overwhelming. Einstein's insights forced us to completely rethink our place in the cosmos, overturning centuries of entrenched beliefs about the very nature of reality itself.Yet Einstein was just getting started. A few years later, he developed his even more mind-bending Theory of General Relativity, which described gravity not as a force, but as a consequence of the curvature of spacetime caused by the presence of mass and energy. This theory not only explained the motion of planets and stars with unprecedented accuracy, but it also laid the groundwork for our modern understanding of black holes, the expansion of the universe, and the existence of gravitational waves – those ripples in the fabric of spacetime itself.Beyond his pivotal role in formulating these world-changing scientific ideas, Einstein's life and philosophies embodied manyof the qualities I most admire. He was a passionate humanitarian who spoke out against racism, nationalism, and militarism throughout his life. He was a gifted writer and thinker whose essays and perspectives transcended the realm of physics and touched on profound questions about the human condition, ethics, and our cosmic significance.I'll never forget one of Einstein's most famous quotes: "The most incomprehensible thing about the universe is that it is comprehensible." This statement beautifully captures both Einstein's profound humility in the face of nature's grandeur, as well as his unwavering faith in our ability as humans to unravel the deepest mysteries of reality through reason, evidence, and unrelenting curiosity. It is this unique combination of qualities –brilliant genius tempered by humility, childlike wonder balanced with rigorous skepticism – that makes Einstein such an inspirational figure to me.Of course, Einstein was far from perfect. His first marriage ended in divorce, and by many accounts he was a less-than-ideal father and husband during certain periods of his life. He also endured many personal and professional struggles, from escaping Nazi persecution to battling depression and loneliness in his later years. But to me, these complexities only makeEinstein's life and accomplishments that much more remarkable – and human.When I think about my own aspirations for the future, I am continuously inspired by Einstein's example. Like him, I hope to maintain an insatiable thirst for knowledge and understanding, to never stop questioning the accepted wisdom, and to approach problems from unorthodox angles. I aim to couple profound insights with sincere humility. Above all, I want to live a life driven by curiosity, a sense of wonder at the marvels of the universe, and the conviction that no truth is so sacred that it should not be scrutinized and tested.Looking back across the vast timeline of human civilization, it's clear that few individuals have influenced our understanding of reality as profoundly as Albert Einstein. His theories opened our eyes to the bizarre cosmic dances of space, time, energy, and matter on scales both microscopic and astronomic. His bold challenges to conventional thinking shattered long-held certainties and illuminated entirely new avenues of inquiry. And his life embodied many of the noblest virtues to which we should all aspire: unrelenting curiosity, critical thinking, humility, compassion, and an unwavering commitment to seeking out universal truths through reason and evidence.In a universe filled with countless brilliant scientists, thinkers, and visionaries across history, Albert Einstein shines as a transcendent figure – both for his unparalleled intellectual achievements and for the iconic example he set for how we can all strive to learn about ourselves and our place in the cosmos. He was far more than just another scientist; he was the personification of humanity's restless drive to know, to understand, to question, and to push the boundaries of knowledge ever outward. That is why Albert Einstein remains my favorite scientist, and likely always will.篇3My Favorite Scientist: Albert EinsteinWhen I was a young kid, I remember seeing pictures of this elderly man with wild grey hair sticking out in all directions. His face seemed kind and friendly, with laughter lines crinkling around his eyes. Little did I know at the time that this man, Albert Einstein, would become one of the most famous scientists of all time - and my personal favorite.As I grew older and began studying science, I became fascinated by Einstein's revolutionary theories and incredible intellect. He didn't just reshape how we view physics, but hiswork impacted fields as diverse as philosophy, mathematics, and even religion. Einstein proved that the universe is a much stranger place than our human intuition would have us believe.Born in 1879 in Germany, Einstein didn't begin speaking until he was three years old, leading his parents to worry that he was disabled. However, it soon became clear that young Albert was simply an deep thinker. He showed a brilliant curiosity from an early age, constant questioning the world around him and performing thought experiments in his mind.At age 16, Einstein wrote his first major scientific work - a carefully researched essay on the behavior of light particles that presaged his revolutionary theories of later years. He sailed through his education, attending university in Zurich, Switzerland, where he graduated in 1900. However, Einstein's unconventional thinking and open defiance of authority made it difficult for him to find an academic job.For years, Einstein took whatever employment he could find, working as a tutor and clerk at the Swiss patent office. During this period of obscurity, he produced some of his most groundbreaking work in his spare time, including his Special Theory of Relativity published in 1905 at age 26. This theoryturned our understanding of space, time, energy and matter upside down.Einstein essentially demonstrated that the laws of physics are the same across all non-accelerating frames of reference, and that the speed of light is independent of the motion of all observers. This led to the famous equation E=mc^2, showing that energy and mass are interchangeable. It revealed that matter can be converted into energy, resulting in the development of nuclear power - both its peaceful and destructive applications.In 1915, Einstein published his even more mind-bending General Theory of Relativity. This audacious hypothesis proposed that gravity is not a force, as Newton believed, but a consequence of the curvature of space and time. It depicted gravity as a warping of the fabric of the universe itself caused by the presence of matter and energy.According to Einstein, massive objects like stars and black holes severely warp the geometry of the space-time continuum, creating gravitational fields that cause other bodies to orbit around them like balls circling a funnel. This crazy-sounding theory was supported by observing how light rays are bent bythe sun's gravitational field - matching Einstein's predictions to astounding accuracy.While the physics world was still absorbing these revolutionary concepts, Einstein made another bombshell announcement in 1917 that fundamentally changed our view of the universe. He hypothesized that the universe itself must be curved, finite and unbounded. This implied a beginning to universal time and space - an expanding cosmos born from an infinitely small, infinitely hot singularity. Einstein's static universe model laid the foundation for modern cosmology and the Big Bang theory.Of course, many dismissed Einstein's outlandish theories as the ravings of a physicist gone mad. He was accused of doing away with absolute space and time, replacing solid Newtonian concepts with subjective and arbitrary principles. His detractors called his work a "terrain of transcendental realms" and produced headlines like "Revolution Dethrones Truth and Reason as Conceived by the Intellect of Man."However, Einstein remained steadfast and confident in his theories, despite the outrage, mockery and hostility from the scientific establishment. He boldly stated, "No fairer destiny could be allotted to any physical theory than that itshould...become a basis for further discoveries." Indeed, his models led to breakthroughs like GPS, nuclear power, and our modern understanding of black holes, neutron stars, and the origins of the universe itself.While his brilliance and insights into the nature of reality are unquestionable, what I admire most about Einstein is his philosophies on life, curiosity and imagination. He recognized the limitations of purely rational, empirical thinking, stating, "The really valuable factor is intuition." Einstein didn't just rely on equations and observations, but dared to imagine wild possibilities that logic and common sense might reject.For example, his famous thought experiment about riding on a beam of light is what sparked his initial insights into the relativity of time and space. Einstein once said, "When a man sits with a pretty girl for an hour, it seems like a minute. But let him sit on a hot stove for a minute - and it's longer than any hour. That's relativity!"Beyond his witty reflections on the pliability of spacetime, Einstein had an almost poetic way of describing the pursuit of knowledge. He recommended, "Never lose a holy curiosity," adding "The important thing is not to stop questioning. Curiosity has its own reason for existing." To Einstein, a burning sense ofawe and wonder was crucial for scientists to keep an open mindset.He also emphasized the importance of imaginative, freeform thinking. Einstein said, "Logic will get you from A to B. Imagination will take you everywhere." He relied heavily on his creativity and visualization skills to conceptualize the complex geometry underlying reality, elegant solutions emerging in his mind's eye. Einstein believed that creativity, not rote calculation, was the key to scientific progress.Another quality that makes Einstein so endearing and inspirational is his humility and humanity. Although he produced world-changing ideas that are difficult for most to grasp, Einstein was down-to-earth and unpretentious. He was an eccentric character, a lovable rebel who went to work in ratty sweaters and slippers. Einstein was famous for his witty sense of humor and wisecracks, once joking, "The difference between stupidity and genius is that genius has its limits."He was also deeply spiritual and philosophical in his views, though not conventionally religious. Einstein had a cosmic sense of awe at the mysteries of the universe, stating, "The most beautiful emotion we can experience is the mystical." He saw science as a path to comprehend the strict laws of nature - anincredible system displaying intelligent design. But Einstein rejected supernatural explanations, maintaining, "What really interests me is whether God had any choice in the creation of the world."In many ways, Einstein emerged as the quintessential scientist - brilliant yet imaginative, curious yet grounded. He revolutionized our understanding of the cosmos through radical thought experiments and unprecedented intuition. Yet Einstein maintained a humility and humanity that made his genius incredibly inspiring and approachable.Looking back, perhaps the universe's most powerful messenger was this wisecracking elderly man with disheveled grey hair and twinkling eyes. Einstein's ability to blend high intelligence with playfulness is why he remains my favorite scientist. His passion for questioning, creativity, and awe at nature's mysteries shaped my own scientific pursuits from a young age. Einstein showed that the path to profound revelations lies not just through numbers and proofs, but through freely exercising our creativity and childlike sense of curiosity about the wonders of our strange universe.。

理解黑洞需要一定的想象力和科学知识英语

理解黑洞需要一定的想象力和科学知识英语Understanding Black Holes Requires a Certain Degree of Imagination and Scientific KnowledgeThe vastness of the universe is a constant source of fascination and wonder for human beings. As we gaze up at the night sky, our eyes are drawn to the twinkling stars, the enigmatic planets, and the mysterious celestial bodies that lie beyond our immediate reach. Among these cosmic enigmas, perhaps none have captured the public's imagination more than the phenomenon known as the black hole.Black holes are regions of space-time where the gravitational pull is so immense that nothing, not even light, can escape their grasp. These cosmic behemoths are the result of the collapse of massive stars at the end of their life cycle. When a star runs out of fuel, its core can no longer support the outward pressure that counteracts the inward pull of gravity, causing it to implode and form a singularity – a point in space-time where the laws of physics as we know them break down.Understanding the true nature of black holes requires a certaindegree of imagination and scientific knowledge. On the surface, the concept of a region of space-time where nothing can escape may seem straightforward, but the deeper one delves into the intricacies of black hole physics, the more complex and mind-bending the subject becomes.One of the key aspects of black holes that challenges our intuitive understanding is the concept of the event horizon. The event horizon is the point of no return – the boundary beyond which nothing, not even light, can escape the gravitational pull of the black hole. Visualizing this invisible barrier and comprehending its significance is a task that requires a significant amount of abstract reasoning.Imagine a person standing on the edge of a cliff, gazing out at the vast expanse of the ocean. As they look down, they can see the waves crashing against the rocks below, but they know that if they were to step over the edge, they would be unable to return. The event horizon of a black hole is analogous to this – it is the point at which the gravitational forces become so overwhelming that even the fastest-moving particles in the universe, photons of light, cannot escape.But the event horizon is just the tip of the iceberg when it comes to the complexities of black hole physics. As one delves deeper into the subject, the challenges to our understanding only grow moreprofound.Consider, for example, the concept of time dilation. According to Einstein's theory of general relativity, the passage of time is affected by the presence of strong gravitational fields. As an object approaches the event horizon of a black hole, the rate at which time passes for that object becomes increasingly slowed down relative to an observer outside the black hole. This means that from the perspective of an external observer, the object appears to be frozen in time, gradually becoming fainter and fainter as it crosses the event horizon.Visualizing this phenomenon requires a significant amount of imagination and a deep understanding of the principles of relativity. It challenges our everyday experience of time and forces us to consider the universe from a radically different perspective – one where the familiar laws of physics no longer apply in the same way.Another aspect of black holes that pushes the limits of our imagination is the nature of the singularity itself. At the center of a black hole, where all the matter and energy of the collapsed star is concentrated, the laws of physics as we know them break down completely. This point of infinite density and infinite curvature of space-time is known as the singularity, and it represents the ultimate limit of our current scientific understanding.Trying to comprehend the singularity, a region where the very fabric of space-time is torn apart, is a task that requires a leap of imagination that few can truly make. It forces us to confront the limitations of our own understanding and to grapple with the fundamental mysteries of the universe.Despite these challenges, the study of black holes has been a cornerstone of modern astrophysics and has led to numerous groundbreaking discoveries. Through the use of sophisticated telescopes and advanced mathematical models, scientists have been able to observe the behavior of black holes in unprecedented detail, shedding light on the most extreme and enigmatic phenomena in the cosmos.From the detection of gravitational waves, the ripples in the fabric of space-time caused by the collision of black holes, to the stunning images of the supermassive black hole at the center of the Milky Way, the study of black holes has pushed the boundaries of our scientific knowledge and our understanding of the universe.But perhaps the greatest contribution of the study of black holes is the way it has challenged our fundamental assumptions about the nature of reality. By confronting us with the limits of our own understanding, black holes have forced us to reckon with thepossibility that there are aspects of the universe that may forever remain beyond our grasp.In this sense, the study of black holes is not just a scientific endeavor, but a philosophical one as well. It reminds us that the universe is a vast and mysterious place, and that our knowledge, no matter how extensive, is always a work in progress. It challenges us to remain humble in the face of the unknown and to continue to explore the limits of our understanding with curiosity, wonder, and a willingness to adapt our perspectives as new evidence emerges.Ultimately, the study of black holes is a testament to the power of the human mind to grapple with the most complex and enigmatic phenomena in the universe. It requires a unique blend of imagination, scientific knowledge, and a willingness to embrace the unknown – qualities that have defined the pursuit of scientific discovery since the dawn of human civilization.。

科技英语阅读与翻译(李健)---unit3 Dark nergy

是什么让我们找了这么久?直到1998年，天文学家们才发现我们所说的暗能量，它几乎是宇宙能量的四分之三，在此之前一直被我们所忽视。暗能量是一种未知的能量形式，围绕在我们每个人的周围，轻轻地推拉我们，掌控宇宙的命运。但是，我们对它却几乎一无所知。确实，一些研究人员此前曾预测存在这类能量，但是他们还是会告诉你，探测暗能量是宇宙学在20世纪最具革命性的发现。暗能量可能不仅是构成宇宙的主体，而且，如果能经受住时间的检验，它将需要提出新的物理理论来支撑。
As astronomers have explored this new phenomenon, they have found that, in addition to determining the overall expansion rate of the universe, dark energy has long-term consequences for smaller scales. As you zoom in from the entire observable universe, the first thing you notice is that matter on cosmic scales is distributed in a cobweblike pattern--a filigree of filaments, several tens of millions of light-years long, interspersed with voids of similar size. Simulations show that both matter and dark energy are needed to explain the pattern.
According to models, dark matter began to clump immediately after the big bang, forming spherical blobs that astronomers refer to as "halos." The baryons, in contrast, were initially kept from clumping by their interactions with one another and with radiation. They remained in a hot, gaseous phase. As the universe expanded, this gas cooled and the baryons were able to pack themselves together. The first stars and galaxies coalesced out of this cooled gas a few hundred million years after the big bang. They did not materialize in random locations but in the centers of the dark matter halos that had already taken shape.

A Holographic Dark Energy Model from Ricci Scalar Curvature

Recent advance in the studies of black hole theory and string theory may provide an inspiration for solving these
problems. It was realized that in quantum gravity, the entropy of a system scales not with its volume, but with
quantum ﬁeld theory. The estimated size of the vacuum energy ρ ≃ ρp where ρp is the Plank density, this is greater than the observed value ρ ≃ 10−123ρp by some 123 orders of magnitude. The coincidence problem is the following:
Alternatively, the particle horizon lP H
=a
t 0
dt/a
could be used as the length scale [6]. However, as S. Hsu [7] and M. Li [8] pointed out, the equation of state for this
its surface area L2, this is the so called holographic principle [4]. To see how this principle could help solve the
cosmological constant problems, we note that in the Einstein equation, Gµν = 8πTµν + Λgµν, where we use the unit system with c=G= =1, the cosmological constant Λ is the inverse of some length squared, [Λ] ∼ l−2, and to be

科技英语阅读（EST

科技英语阅读（EST科技英语阅读（EST Reading）课后习题答案Unit 1 MathematicsPart I EST Reading1. Who is Bertrand Russell?Bertrand Arthur William Russell (b.1872 –d.1970) was a British philosopher, logician, essayist and social critic best known for his work in mathematical logic and analytic philosophy. His most influential contributions include his defense of logicism (the view that mathematics is in some important sense reducible to logic), his refining of the predicate calculus introduced by Gottlob Frege (which still forms the basis of most contemporary logic), his defense of neutral monism (the view that the world consists of just one type of substance that is neither exclusively mental nor exclusively physical), and his theories of definite descriptions and logical atomism. Russell is generally recognized as one of the founders of modern analytic philosophy, and is regularly credited with being one of the most important logicians of the twentieth century.2. What is Russell’s Paradox?Russell discovered the paradox that bears his name in 1901, while working on his Principles of Mathematics (1903). The paradox arises in connection with the set of all sets that are not members of themselves. Such a set, if it exists, will be a member of itself if and only if it is not a member of itself. The paradox is significant since, using classical logic, all sentences are entailed by a contradiction. Russell's discovery thus prompted a large amount of work in logic, set theory, and the philosophy and foundations of mathematics.Section C Post-reading TaskReading Comprehension1. Directions: Work on your own and fill in the blanks with the main idea.Part 1 (Para. 1): Brief introduction to Russell’s paradoxPart 2 (Paras. 2-5): The effect of Russell’s paradox on Gottlob Frege’s system.Para. 2: Russell’s paradox dealt a heavy blow to Frege’s attempts to develop a foundation for all of mathematics using symbolic logic.Para. 3: An illustration of Russell’s parado x in terms of sets Para. 4: Contradiction found in the set.Para. 5: Frege noticed the devastating effect of Russell’s paradox on his system and inability to solve it.Part 3 (Paras. 6-8): Solutions offered by mathematicians to Russel’s paradoxPara. 6: Russell’s own response to the paradox with his "theory of types."Para. 7: Zermelo's solution to Russell's paradoxPara. 8: What became of the effort to develop a logical foundation for all of mathematics?Part 4 (Para. 9): Correspondence between Russell and Frege on the paradoxVocabulary and Structure2. Directions: Complete the sentences with the words given in the brackets. Change the form if necessary.1) The key to unraveling such apparent paradoxes is to characterize the initial set of possibilities ("initial" meaning before you receive any extra information) and then to eliminate possibilities based on that extra information. (base)2) Indeed, this separation of meaning is reflected by the definition of "weak" in the OALD, with adistinct sense reserved for its use when pertaining to that of solutions (definition)3) The resulting radical pollution control programme outlined by Nixon, calling for a 90 per cent reduction in vehicle emissions by 1980, not only led to him being credited (albeit briefly) as policy initiator of an environmental clean-up but also provided him with the chance to deal a blow to one of his most important opponents in the 1972 elections, Edmund Muskie (blow)4) Singapore's continuing investments in education and training has brought a tenfold increase in our pool of Information Technology professionals and the Singapore worker has been consistently rated by BERI as the world's best in terms of technical skills, attitude and productivity. (term)5) In this work he was led to topology, a still new kind of mathematics related to geometry, and to the study of shapes (compact manifolds) of all dimensions. (lead)6) If there is no allowable string which spans the whole graph, then we can search in the same way as described above, but wherever the required path does not exist in the tree, check if that position in the tree is flagged for end-of-word (way)7) During the past century, steps forward in physics have often come in the form of newly found particles; in engineering, more complex devices; in astronomy, farther planets and stars; in biology, rarer genes; and in chemistry, more useful materials and medications. (form)8) A second reason for measurements is the more theoretical, put by Love as " the discovery of numerical relations between thequantities that can be measured to serve as a basis for the inductive determination of the form of the intrinsic energy function. " (serve)9) Thus the optimum conditions for coastal terrace development would seem to be areas with small tidal ranges. Finally, tidal range is an important factor in the generation of tidal currents which may locally become of geomorphological importance (become)10) The original double entrance doors to the booking hall had been replaced by an utterly incongruous picture window as had adjacent booking hall and waiting room windows. (replace)3. Directions: Reorder the disordered parts of a sentence to makea complete sentence.1) A simple way to describe topology is as a 'rubber sheet geometry' — topologists study those properties of shapes that remain the same when the shapes are stretched or compressed.2) Since the mid-1990s scientists have floated the idea that representations of numeric quantities, whether expressed as digits or as written words, are codified by the parietal cortex, a higher-processing region in the brain located just above the forehead.3) As activity was monitored, located just above the forehead ,researchers noted changes under the assumption that the brain reduces activity as it becomes accustomed to a stimulus and then reactivates when a novel stimulus is presented.4) That has not stopped physicists from devising new algorithms for the devices, which can calculate a lot faster than ordinary computers—in fact, exponentially faster, in quite a literal sense.5) Such a device would be made of metamaterial, a thicket ofmetal rings or other shapes that bends light in funny ways.4. Directions: Change the following sentences into nominalized ones.1) The passage of night could be marked by the appearance of 18 of these stars.2) The full proof of Fermat's Last Theorem is contained in these two papers.3) The concept of fixed-length hours, however, did not originate until the Hellenistic period.4) There is a probability that my first sock is red because only one of the remaining three socks is red.5) The importance of accurate data in quantitative modeling is central to using Bayes's theorem to calculate the probability of the existence of God.Discourse Understanding1. C. A "3 percent margin of error" means that there is a 95 percent chance that the survey result will be within 3 percent of the population value.2. E. How is it that a survey of only 1,000 people can reach this level of accuracy?3. G. The margin of error depends inversely on the square root of the sample size.4. A. The margin of error is a mathematical abstraction, and there are a number of reasons why actual errors in surveys are larger.5. F. Finally, the 3 percent margin of error is an understatement because opinions change. Section A Pre-reading Task1. Who discovered the Mandelbrot set?This is not a trick question, not easy to answer. Many peopleincluding Mandelbrot have laid claim to the discovery.2. Why was the set named after Benoit B. Mandelbrot?The set is named after Benoit B. Mandelbrot, a mathematician at the IBM Thomas J. Watson Research Center because he coined the term fractal to describe phenomena (such as coastlines, snowflakes, mountains and trees) whose patterns repeat themselves at smaller and smaller scales.3. Why has there been so much controversy about who discovered the Mandelbrot set? Mandelbrot claims that he and he alone discovered the Mandelbrot set, but there are other mathematicians who have challenged his claim.4. What did the challengers say abo ut Mandelbrot’s claim of discovery?Two mathematicians said that they independently discovered and described the set at about the same time as Mandelbrot did. And another mathematician also asserted that his work on the set not only predated Mandelbrot's efforts but also helped to guide them5. Why did some professors support Mandelbrot’s claim?Mandelbrot deserves to have the set named after him, because his efforts brought the set to the attention of both the public and of the pure-mathematics community.Section C Post-reading TaskLanguage in Use1. Match the Chinese in the left column with the English in the right column.迭代函数iterative function优先权之争priority battle分形特征fractal properties有意义make sense以越来越小的规模重复同一模式patterns repeat themselves at smaller and smaller scales混沌理论chaos theory季刊a quarterly journal数学界the mathematics community波纹线crisp lines会议公报proceedings of a conference2. Join the following short sentences into longer ones.e.g. a. A fractal is generally a rough or fragmented geometric shape .b. The shape can be subdivided in parts.c. each part is (at least approximately) a reduced-size copy of the whole, a property calledd. each part has a property of self-similarity.e.g. A fractal is generally "a rough or fragmented geometric shape that can be subdivided in parts, each of which is (at least approximately) a reduced-size copy of the whole", a property called self-similarity.1) In addition to coining the term "fractal" to describe objects and surfaces which are irregular at various dimensions of scale, he also introduced such concepts as "fractal dimensions" and the particular fractal known as the Mandelbrot set, frequently represented with the mathematical formula z → z2 + c.2) It appeared that things were settling into a pleasant and fruitful routine, with his school lessons supplemented by long talks with his uncle about classical analysis, the iterative work of Pierre Fatou and the equally fascinating Julia Sets generated by Gaston Julia3) Just as the youthful Mandelbrot had passed his college entrance exams by translating algebraic problems intogeometrical problems, and solving them by intuitively deducing the "perfected" shape, he here realized there was something deeper, something mathematical, behind these strange patterns.4) But the beauty in Mandelbrot's models was not that they generated a deceitful randomness, but that they could generate graphed data whose visual pattern accurately mimicked the visual patterns created by real phenomena。

A MODEL OF THE DARK MATTER DISTRIBUTION

;
References
1. P.J.E. Peebles in The Large Scale Structure of the Universe, (Princeton University Press, Princeton, 1980). 2. J. R. Bond et al., Ap. J. 379, 440 (1991). 3. H. Mo & S. D. M. White, MNRAS 282, 347 (1996). 4. R. K. Sheth, MNRAS , submitted (1997a). 5. E. Schrodinger, Phys. Zeit. 16, 289 (1915). 6. S. Colombi et al., MNRAS 287, 241 (1997). 7. R. K. Sheth, MNRAS , submitted (1997b). 2Biblioteka RAVI K. SHETH
The comoving size R of any given region changes due to gravitational instability. Assume that the evolution of the size R is given by a model, e.g., spherical collapse.1 For a given region, such a model provides relations between the initial size R0 , the initial overdensity 0 , the time z , and the evolved Eulerian size R(z ). For example, if given R0 , 0 , and z , then R(R0 ; 0 ; z ) is determined. If only R and z are given, then the model describes a curve in the (R0 ; 0 ) plane: 0 (R0 jR; z ). Call this curve 0 (R0 jR; z ) the barrier B (R; z ). In the spherical collapse model, B (R; z ) ! constant as R ! 0 for all z . De ne B (0; z ) c (z ). If z1 < z2 then c (z1 ) < c (z2 ). The Eulerian probability distribution function p(M0 jR; z ) is the fraction of regions of size R that, at z , contain mass M0 . To estimate this pdf, rst assume 3 that the initial uctuation 0 is small, so M0 = V0 = R0 . Next, assume the initial distribution of uctuations p( 0 jR0 ) is Gaussian. Then choose a random position in the initial Gaussian eld. Compute 0 in spheres R0 centred on this position. Call the curve 0 (R0 ) centred on this position a trajectory. This trajectory may intersect the barrier B (R; z ) many times. Find the largest value of R0 at which the trajectory intersects B (R; z ). Call this the rst crossing 3 of B (R; z ). Recall that M0 = R0 : mass and initial volume are equivalent. So, this trajectory represents a volume element of a region containing mass 3 M0 . Initially, M0 had size R0 and overdensity 0 (R0 jR; z ). At z , it has size R. Repeat for an ensemble of such trajectories. So compute the distribution of rst crossings of B (R; z ). The fraction of trajectories which rst cross the barrier B (R; z ) at R0 represents the fraction of mass that is in objects of mass M0 that, at z , have size R. From this, the average number density n(M0 jR; z ) of such regions can be computed easily. Assume that the number of such regions is conserved. Then n(M0 jR; z ) is the same as p(M0 jR; z ). When R = 0, then the barrier height is constant, and the rst crossing distribution is known.2 Equate the fraction of trajectories which rst cross B (0; z ) = c (z ) at R0 with the fraction of mass in regions M0 that, at z , have 1

Can the Existence of Dark Energy Be Directly Detected

Thirty-Fourth International Conference on High Energy Physics, Philadelphia, July 29-August 5 2008Can the Existence of Dark Energy Be Directly Detected?Martin L. PerlStanford Linear Accelerator Center and Kavli Institute for Particle Astrophysics and CosmologyStanford University, 2575 Sand Hill Rd. Menlo Park, CA 94025, USAThe majority of astronomers and physicists accept the reality of dark energy and also believe that it can only be studied indirectly through observation of the motions of stars and galaxies. In this paper I open the experimental question of whether it is possible to directly detect dark energy through the presence of dark energy density. Two thirds of this paper outlines the major aspects of dark energy density as now comprehended by the astronomical and physics community. The final third summarizes various proposals for direct detection of dark energy density or its possible effects. At this time I do not have a fruitful answer to the question: Can the Existence of Dark Energy Be Directly Detected?1. DARK ENERGY DETECTION: AN EXPERIMENTAL PROBLEM1.1. Magnitude of Dark Energy DensityMany physicists and astronomers do not realize that the dark energy density, ρDE, is not infinitesimal by the standards of the modern laboratory. Recall that the critical energy of the universe is presently taken to be ρc = 9×10-10 J/m3, and using ρDE = 0.70×ρc we obtainρDE = 6.3×10-10 J/m3and in mass per unit volume ρDE →0.70×10-26 kg/m3 = 3.9 GeV/c2 m3 ~ 4 protons/m3. I use MKS units to emphasize that I am thinking about an experimental question. To think about the magnitude of ρDE, I compare it to an electric field of E=1 volt/m. This electric field energy density isρE = ε0Ε2/2= 4.4×10-12J/m3This size electric field is easily detected and measured. Thus in the laboratory and in space we detect and measure electric fields whose energy densities are much less than ρDE. This realization was the impetus for me to consider the possibility of direct detection of ρDE or its effects.It is important to compare ρDE with the energy density of the gravitational fieldρG = g2/(8πG N) = 5.7×10+10J/m3 on the earth’s surfacewhere g is the gravitational acceleration and G N is Newton’s gravitational constant. Thus on the earth’s surfaceρG is enormous compared to ρDE.1.2. Obvious Problems in Direct Detection and Measurement of Dark Energy DensityThere are obvious problems in the direct detection and measurement of dark energy density:•Unlike the electric field the dark energy field cannot be turned off and on.•We expect that the dark energy field is uniformly distributed; hence we do not expect to find a region with zero dark energy. But it is possible that the distribution is not uniform, that there are regions of larger and smaller density in space.•In some hypothesis about the nature of dark energy, the dark energy field does not exert a force on any material object. Hence there would be no way to detect it.•As calculated in the previous subsection, ρG at the earth’s surface is enormous compared to ρDE, therefore a proposed dark energy detection method that is sensitive to gravity cannot be carried out on the earth’s surface. The experiment would have to be carried out in space, sufficiently far from the sun as well as the planets.1.3. Dark Energy and the Planck ScaleNumerous discussions of dark energy are involved with the Planck scale with the so called Planck mass, M Planck, and the Planck energy, E Planck, given byM Planck= [hc/2πG N]1/2 = 1.2×1019 GeV/c2 = 2.2×10-8 kgE Planck= [hc5/2πG N]1/2 = 1.2×1019 GeV = 2.0×109 JHere h is Planck’s constant and c is the velocity of lightI am bothered by the prevalent use of E Planck in dark energy discussions. E Planck mixes a quantum mechanical constant with two classical constants, yet ignores another classical constant - the electron charge, e, that incorporates the mystery of the quantization of electric charge. Of course it common to say that the Planck energy is the region where quantum mechanics intimately intersects with general relativity and I agree with that vague idea. But what does the Planck energy have to do with dark energy? We do not know if dark energy has anything to do with gravitation. I return to this later when I summarize the infamous problem that arises when dark energy is associated with ground state vacuum fluctuation energy and E Planck is used as a cut-off.1.4. Mass Scales, Length Scales and Dark Energy1.5.1. Review of Mass and Length Scales ConceptAn early example of the use of mass and length scales is the astonishing use made by Yukawa to interpret the strong force as caused by pion exchange. We write the strong potential, V, as a function of the distance r from the potential source in the simplified form:V = -a exp(r/L strong)where a gives the strength of the potential, and L strong is the range or length scale. The general quantum mechanical relation between L and the mass m of the particle carrying the force ism×L = h/(2πc) (1) It is convenient to remember that h/(2πc)= 1.97×10-13 MeV/c2 m = 3.51×10-43 kg m. Thus for the strong force with L strong =10-15 m, we get the pion mass = 197 MeV/c2, as Yukawa predicted seventy years ago.1.5.2. Mass and Length Scales for the Weak InteractionEquation 1 works well for the weak force if we use m≈100 GeV/c2 to approximate the W and Z0 masses. Then Eq. 1 gives L weak≈ 2×10-18 m, much smaller than the strong force range as it should be.1.5.3. Mass and Length Scales at the Planck ScaleUsing Eq.1 and M Planck = 2.2×10-8 kgL Planck = 1.6×10-35 m.This length dominates string theory concepts and much theoretical work on quantum gravity1.5.4. Mass and Length Scales for Dark EnergyWe do not know a mass m for dark energy to insert in the general quantum mechanical relation of Eq. 1 to calculateL DE. We only know the dark energy density, ρDE . Therefore we resort to a dimensional argument,L DE = [hc/(2πρDE)]1/4 = 80×10-6 m = 80μm,that may have no validity. But probing dark energy is so difficult that we temporarily accept the idea. L DE corresponds to a frequencyf DE = c/ L DE = 4×1012 Hz.Note that in both of these two equations the presence or absence of factors of 2 and π are arbitrary.For later use we writeρDE = [h/(2πc3)] f DE4 (2)2. DARK ENERGY AND THE VACUUM ENERGY DENSITY2.1. The Puzzle of the Connection Between Vacuum Energy Density and Dark Energy IfThere Is a ConnectionConventional quantum mechanics requires that a ground state have non-zero energy. Following Ref. [1], a massless scalar field has ground state energies ½h f1, ½h f2 ½h f3... when the field is treated as an harmonic oscillator. The total vacuum energy density ρvac is obtained by quantizing the system in a cubic box and integrating up to some cutoff frequency f max, yieldingρvac = [hπ/(2c3)]f max4 (3)Note that Eqs. 2 and 3 are the same except for factors of 2 and π.Eq. 3 leads to an infinite quantity unless f max is finite. Using an argument I don’t like because of my mistrust of the significance of the Planck scale, it is conventional to set f max = f Planck ~ 1043 Hz. This leads to the result that has been repeated ad nauseam, ρvac/ρDE ~ (f max/ f DE)4 ~ 10120, an unacceptable result that bedevils the idea of a connection between vacuum energy and dark energy.2.2. Some Proposed Cures to the PuzzleSome proposed cures are:•Assume that since in reality there are many different fields, their contributions cancel each other exquisitely giving a small net ρvac. An impetus for this concept is the known phenomenon that bosons and fermionshave opposite sign contributions to ρvac.•Find a reason for f max to be much less than f Planck.•Make a dark energy model that has nothing to do with vacuum energy.•Question the reality of vacuum energy and so disconnect from theories about dark energy [2].3. PROPOSALS FOR DIRECT DETECTION OF DARK ENERGY OR ITS EFFECTS3.1. Superconductor Noise and Dark EnergyBeck and Mackey [3] have proposed (a) that dark energy is only connected to electromagnetic vacuum energy density with a cutoff above 4×1012Hz and (b) that this idea can be tested by looking for a decrease above 4×1012 Hz in the noise spectrum in superconductors. This proposal has been substantially criticized [4].3.2. Dark Energy and Measurements of Gravitational Force at Small DistancesIn the past fifteen years there have been several short distance measurements [5-7] of the validity of the inverse square law for the gravitational force. Distances of the order of 50 to 100 μm have been examined. One motivation for these experiments was predictions about the effect of hypothetical string theory extra dimensions on gravity. Another motivation was the possible significance of the dark energy length scale L DE = 80 μm, deduced in Sec. 1.5.4. It is usual to generalize the Newtonian gravitational equation as follows:V(r) = -G N (m1m2/r) [1+a exp(-r/λ)],where a and λ are parameters for the deviation from Newtonian physics. No deviations have been found [5-7].3.3. Might the Dark Energy Density Be Clumped?At present my thoughts are concentrated on the possibility that ρDE is not uniformly distributed, and that the clumping can be detected in space, sufficiently far away from the gravitational fields of the sun and planet s. The burning question is what can do the detection. For electromagnetic fields we have particles charge, for gravitational fields we have particle mass, but what particle property is sensitive to the dark energy field? This is the fundamental experimental question in dark energy physics. For example, what is the possibility of dark energy producing a phase shift in an atom, and using atom interferometry to detect the phase shifts?3.4. Might There Be A Dark Energy Particle?In the multitudinous world of dark energy theories the idea that there might be a dark energy particle [8] is an outlier theory. But the experimenter should think even about outliers.3.5. An Experimenter’s ConclusionAt the start of the nineteenth century physicists worked on three apparently unrelated phenomena: electricity,magnetism, light. By the end of the nineteenth century these phenomena had been united into electromagnetic theory.At the start of the twenty first century we work on gravitation, dark matter, dark energy, and many problems having to do with the nature of mass. I am optimistic that we will be as productive in fundamental astronomy and physics in the future as we have been in the last two centuries.ACKNOWLEDGMENTSI thank Garrett Morton for his participation in the preparation of this paper. I have had particularly usefulconversation on the nature of dark energy with Frans Klinkhamer, Philip Mannheim, Mark Trodden, Thomas Rizzo, Marvin Weinstein and Helen Quinn. This work was supported by Department of Energy contract DE-AC03-76SF00515.References[1] L. Bergstrom and A. Goobar, Cosmology and Particle Physics, 2nd Ed., (Springer, Berlin, 2004) p. 126.[2] S. Saunders, “Is the Zero-Point Energy Real” in Ontological Aspects of Quantum Field Theory (World Scientific,Singapore, 2002), Eds. M. Kuhlmann, H. Lyre, A. Wayne.[3] C. Beck and M. C. Mackey, Int. J. Mod. Phys., D17, 71 (2008)[4] P. Jetzer and N. Straumann, Phys. Lett., B639, 47 (2006); Phys. Lett. B606, 77 (2005).[5]J.C. Long and J.C. Price, C. R. Physique 4, 337 (2003); H. W. Long et al., Nature 421:922 (2003).[6] A. A. Geraci et al., Phys. Rev. D78, 022002 (2008).[7] D. J. Kapner et al., Phys. Rev. Lett. 98, 021101 (2007)[8] A. de la Macorra, Phys. Rev., D72, 043508 (2005); S. DeDeo, Phys. Rev. D73, 043520 (2006).。

2020年职称英语理工类完形填空辅导(5)

2020年职称英语理工类完形填空辅导(5) Dark Forces Dominate UniverseThe earth, moon, sun and all visible stars in the sky make up less than one percent of the universe. Almost all the rest is dark matter and dark energy, unknown forces that (51) astronomers.Observations in recent years have changed the basic(52)of how the universe evolved and have indicated how little is known about the major forces and substances that (53) our world.Astronomers now know that luminous(发光的)matter-stars，planets and hot gas ―― Accounts (54) only about 0,4 percent of the universe. Non-luminous components, such as black holes and intergalactic(星系间的)gas, (55)up 3.6 percent The restis either dark matter, about 23 percent, or dark energy, about 73 percent.Dark matter, Sometimes (56)" cold dark matter, has been known for some time. Only recently have researchers come to understand the key role it (57)formation of stars, planets and even people."We (58) our very existence to dark matter," said physicist Paul Steinhardt and a co-author of a review on dark matter which (59)not long ago in the journal Science."Dark matter dominated the structure(60)in the early universe," Steinhardt said.''For the first few billion years dark matter contained most of the mass of the universe You can think of ordinary matter (61) a froth(泡沫)of an ocean ofdark matter.The dark matter dumps(结成块)and the ordinary matter falls into it.That (62) to the formation of the stars and galaxies(星系)."Without dark matter, "there would be virtually no structures in the universe."The nature of dark matter is (63)It cannot be seen or detected directly astronomers know it is there because of its (64)on celestial(天体的)objects that can be seen and measured.But the most dominating force of all in the universe is called dark energy, a recently (65)power that astronomers say is causing the galaxies in the universe to separate at a faster and faster speed.51 A worry B move C puzzle D reject52 A understanding B value C pattern D structure53 A changed B described C designed D shaped54 A in B for C of D to55 A make B keep C set D get56 A written B called C identified D seen57 A signed B stressed C acted D played58 A believe B owe C feel D regard59 A appeared B carried C published D contributed60 A element B shape C formation D power61 A with B as C form D beside62A turned B worked C led D attempted63 A unknow B interesting C different D visible64 A form B outcome C effect D source65 A seized B proven C caught D grasped答案：51 C puzzle：使……感到迷惑。

Observational Tests of Modified Gravity

a r X i v :0709.2375v 1 [a s t r o -p h ] 17 S e p 2007Observational Tests of Modiﬁed GravityBhuvnesh Jain 1&Pengjie Zhang 2,3∗1Department of Physics and Astronomy,University of Pennsylvania,Philadelphia,PA 191042Shanghai Astronomical Observatory,Shanghai,China 2000303Joint Institute for Galaxy and Cosmology (JOINGC)of SHAO and USTCModiﬁcations of general relativity provide an alternative explanation to dark energy for the ob-served acceleration of the universe.Modiﬁed gravity theories have richer observational consequences for large-scale structure than conventional dark energy models,in that diﬀerent observables are not described by a single growth factor even in the linear regime.We examine the relationships be-tween perturbations in the metric potentials,density and velocity ﬁelds,and discuss strategies for measuring them using gravitational lensing,galaxy cluster abundances,galaxy clustering/dynamics and the ISW eﬀect.We show how a broad class of gravity theories can be tested by combining these probes.A robust way to interpret observations is by constraining two key functions:the ratio of the two metric potentials,and the ratio of the Gravitational “constant”in the Poisson equation to Newton’s constant.We also discuss quasilinear eﬀects that carry signatures of gravity,such as through induced three-point correlations.Clustering of dark energy can mimic features of modiﬁed gravity theories and thus confuse the search for distinct signatures of such theories.It can produce pressure perturbations and anisotropic stresses,which breaks the equality between the two metric potentials even in general relativity.With these two extra degrees of freedom,can a clustered dark energy model mimic modiﬁed gravity models in all observational tests?We show with speciﬁc examples that observational constraints on both the metric potentials and density perturbations can in principle distinguish modiﬁcations of gravity from dark energy models.We compare our result with other recent studies that have slightly diﬀerent assumptions (and apparently contradictory conclusions).PACS numbers:98.65.Dx,95.36.+x,04.50.+hI.INTRODUCTIONThe energy contents of the universe pose an interesting puzzle,in that general relativity (GR)plus the Standard Model of particle physics can only account for about 4%of the energy density inferred from observations.By in-troducing dark matter and dark energy,which account for the remaining 96%of the total energy budget of the universe,cosmologists have been able to account for a wide range of observations,from the overall expansion of the universe to the large scale structure of the early and late universe [1].The dark matter/dark energy scenario assumes the va-lidity of GR at galactic and cosmological scales and in-troduces exotic components of matter and energy to ac-count for observations.Since GR has not been tested independently on these scales,a natural alternative is that the failures of GR plus the Standard Model of par-ticle physics imply a failure of GR.This possibility,that modiﬁcations in GR at galactic and cosmological scales can replace dark matter and/or dark energy,has become an area of active research in recent years.Attempts have been made to modify GR at galactic [2]or cosmological scales [3,4,5].Modiﬁed Newtonian Dynamics (MOND)and its relativistic version (Tensor-Vector-Scalar,TeVeS)[2]are able to replace dark matter at galaxy scales to reproduce the galaxy rotation curves,2fers[6,7,8,9,10,11,12,13,14,15,16,17,18]from that in GR.Theories of LSS in these modiﬁed gravity models are still in their infancy.However,perturbative calcula-tions at large scales have shown that it is promising to connect predictions in these theories with observations of LSS.Most studies have focused on probes of a single growth factor with one or a few observables.In this paper we will consider a variety of LSS observables that can be measured with high precision with current or planned surveys.Our emphasis will be on model-independent constraints of MG enabled by combining diﬀerent ob-servables.Carrying out robust tests of MG in practice is chal-lenging as in the absence of a fundamental theory,the modiﬁcations to gravity are often parameterized by free functions,to beﬁne tuned andﬁxed by observations. Given the parameter space available to both DE and MG theories,it is unclear how the two classes of theories can be distinguished.Kunz and Sapone[19]presented a rather pessimistic example.They found that one can tune a clustered dark energy model to reproduce obser-vations of gravitational lensing and matterﬂuctuations in the DGP model.It is not clear if this conclusion ap-plies to all modiﬁed gravity models and if adding more LSS observables helps to break this severe degeneracy. In this paper,weﬁrst discuss ways of parameterizing modiﬁed gravity models and dark energy models.§II presents the deﬁnitions and evolution equations for per-turbations in the metric and the energy momentum ten-sor.We then classify independent LSS observables based on the perturbations that are probed by them.§III is devoted to the use of observational probes of LSS for testing MG.We consider the four fundamental pertur-bation variables and the observations that can be used to probe them.The additional information available in the quasilinear regime is discussed in the Appendix.In §IV we consider the question of distinguishing MG from DE scenarios.The speciﬁc question we want to answer is:given a set of LSS observations,can a general MG model be mimicked by a DE model?If not,what LSS observables are required to break the degeneracy?We conclude in§V.II.PERTURBATION FORMALISMBy deﬁnition,the dark sector(dark matter and dark energy)can only be inferred from their gravitational con-sequence.In general relativity,gravity is determined by the total stress-energy tensor of all matter and en-ergy(Gµν=8πG Tµν).Thus we can treat dark mat-ter and dark energy as a single entity,without loss of physical generality[20,21,22].This entity has total mean matter density¯ρGR and equation of state parame-ter w=p GR/¯ρGR.However,when discussing perturba-tions in this entity,we may separate it into a matter com-ponent(dissipationless particles which can be described as a pressure-lessﬂuid free of anisotropic stress)and a dark energy component.Throughout this paper,when we refer to“smooth”or“clustered”dark energy,we re-fer to this dark energy subset of the overall dark sector. We may consider the Hubble parameter H(z)to be ﬁxed by observations.In a dark energy model,¯ρGR is given by the Friedman equation of GR:¯ρGR=3H2/8πG. The equation of state parameter is w=−1−2˙H/3H2. The corresponding modiﬁed gravity model has mat-ter density¯ρMG to be determined from its Friedman-like equation.We will consider MG models dominated by dark matter and baryons at late times and denoteﬂuid variables such as the density with subscript MG.A.Metric andﬂuid perturbationsWith the smooth variablesﬁxed,we will consider per-turbations as a way of testing the models.In the Newto-nian gauge,scalar perturbations to the metric are fully speciﬁed by two scalar potentialsψandφ:ds2=−(1+2ψ)dt2+(1−2φ)a2(t)d x2(1) where a(t)is the expansion scale factor.This form for the perturbed metric is fully general for any metric the-ory of gravity,aside from having excluded vector and tensor perturbations(see[24]and references therein for justiﬁcations).Note thatψcorresponds to the Newto-nian potential for the acceleration of particles,and that in General Relativityφ=ψin the absence of anisotropic stresses.A metric theory of gravity relates the two potentials above to the perturbed energy-momentum tensor.We in-troduce variables to characterize the density and velocity perturbations for aﬂuid,which we will use to describe matter and dark energy(we will also consider pressure and anisotropic stress below).The densityﬂuctuationδis given byδ( x,t)≡ρ( x,t)−¯ρ(t)3 modiﬁed gravity models from dark energy.Each has ascale and redshift dependence,so it is worth noting whichvariables and at what scale and redshift are probed bydiﬀerent observations.It is convenient to work with theFourier transforms,such as:ˆδ( k,t)= d3xδ( x,t)e−i k· x(4)When we refer to length scaleλ,it corresponds to aa statistic such as the power spectrum on wavenumberk=2π/λ.We will henceforth work exclusively with theFourier space quantities and drop theˆsymbol for conve-nience.B.Evolution and constraint equationsWe consider here theﬂuid equations for DE and MGscenarios.We work in the Newtonian gauge and followthe formalism and notation of[20],except that we usephysical time t instead of conformal time.We are inter-ested in the evolution of perturbations after decoupling,so we will neglect radiation and neutrinos as sources ofperturbations.We will make the approximation of non-relativistic motions and restrict ourselves to sub-horizonlength scales.One can also self-consistently neglect timederivatives of the metric potentials in comparison to spa-tial gradients.These approximations will be referredto as the quasi-static,Newtonian regime.We will notconsider the evolution of perturbations on super-horizonlength scales;[23]show that diﬀerences in their evolutionmay have observable consequences for some MG models(discussed further under the CMB below).1.Dark Energy with GR scenarioWeﬁrst consider the DE scenario,assuming -ing the perturbedﬁeld equations of GR toﬁrst ordergives a set of constraint and evolution equations.Theevolution of the density and velocity perturbations in-cludes gravity and pressure perturbationsδp as sources.In the Newtonian limit they give the familiar continuityand Euler equations for a perfectﬂuid.Keeping allﬁrstorder terms,and using the notation˙δ≡dδ/dt,gives:˙δGR =−(1+w)(θGRρ+3HwδGR≃−(1+w)θGRρ+3HwδGR.(5)In the second line we have dropped the˙φterm as it is negligible compared to the other terms in the quasi-static regime.The Euler equation is given by˙θGR =−H(1−3w)θGR−˙w1+w−σ+ψ k2k2 .≃−4πGa2¯ρGRδGR(7)where in the second line we have dropped the HθGR/k2term as it is negligible for nonrelativistic motions onscales well below the horizon.Non-zero anisotropic stressσleads to inequality be-tween the two potentials:k2(φ−ψ)=12πGa2(1+w)¯ρσ.(8)It is common to takeφ=ψfor ordinary matter anddark matter;however clustered dark energy can have anon-negligible anisotropic stress.Eqns.5-8fully describe the evolution of perturbationsin DE scenarios in the quasi-static,Newtonian regime.Next we consider the analogous relations for modiﬁedgravity scenarios.2.Modiﬁed Gravity scenarioFor minimally coupled gravity models with baryonsand cold dark matter,but without dark energy,we canneglect pressure and anisotropic stress terms in the evo-lution equations to get the continuity equation:˙δMG=− θMG a,(9)where the second equality follows from the quasi-staticapproximation as for GR.The Euler equation is:˙θMG=−HθMG+k2ψ4equation and a second equation connectingφandψ[25]. Weﬁrst write the generalization of the Poisson equation in terms of an eﬀective gravitational constant G eﬀ:k2φ=−4πG eﬀ(k,t)¯ρMG a2δMG.(11) Note that the potentialφin the Poisson equation comes from the spatial part of the metric,whereas it is the “Newtonian”potentialψthat appears in the Euler equa-tion(it is called the Newtonian potential as its gradient gives the acceleration of material particles).Thus in MG, one cannot directly use the Poisson equation to eliminate the potential in the Euler equation.A more useful ver-sion of the Poisson equation would relate the sum of the potentials,which determine lensing,with the mass den-sity.We therefore introduce˜G eﬀand write the constraint equations for MG ask2(ψ+φ)=−8π˜G eﬀ(k,t)¯ρMG a2δMG(12)φ=ψη(k,t)(13) where˜G eﬀ=G eﬀ(1+η−1)/2.Note that if one starts in real space then the corresponding parameters would not be Fourier transforms ofηand˜G eﬀ.Thus the Fourier transform of the PPN parameterγ≡φ/ψ,the ratio of the metric potentials in real space constrained by solar system tests,is given by a convolution ofηandψ[81]. Only ifηis scale independent would it be the Fourier transform ofγ.A similar reasoning applies to˜G eﬀin using the Poisson equation.We prefer to work in Fourier space because of the ease of describing perturbations: each Fourier mode evolves independently in the large-scale,linear regime.Furthermore,the equations describ-ing cosmological perturbations in MG theories such as f(R)gravity and DGP are generally expressed in Fourier space.The parameter˜G eﬀcharacterizes deviations in the (ψ+φ)-δrelation from that in GR.Since the combination ψ+φis directly responsible for gravitational lensing,˜G eﬀhas a speciﬁc physical meaning:it determines the power of matter inhomogeneities to distort light.This is the reason we prefer it over working with more direct gener-alization of Newton’s constant,G eﬀ.The˜G eﬀ-ηparameterization is equivalent to the Q-ηparameterization independently proposed by[18],where Q parameterizes deviations in Poisson equation(7)from GR.For minimally coupled gravity models,with no dark energyﬂuctuations,it is also equivalent to that proposed by[16].Andηis also equivalent to the parameter̟pro-posed by[17].DGP and f(R)gravity can be described by our parameterization.So as the widely adopted Yukawa potential.An exception to our approach is TeVeS as it includes scalar and vectorﬁelds that are coupled to the growth of scalar perturbations.For a generic metric theory of MG,one would expect that a Poisson-like equation is valid to leading order in the potentials and the density perturbation,at least on large scales in the linear regime where Fourier modes are uncoupled.In this regime,we expect that since the left-hand side of theﬁeld equations involve curvature,it must have second derivatives of the metric perturbations,while the right hand side is simply given by the energy mo-mentum tensor.On smaller scales,in general a MG the-ory may not obey superposition and require higher order terms and higher derivatives of the potentials.Similarly a generic relation betweenφandψis likely to have a lin-earized relation of the form in Eqn.13.While it is not necessary that the leading term be linear in both the po-tentials,observational constraints require that it be very close to linear withη≃1on small scales where tests of gravity exist(see[26]for a review).With the linearized equations above,the evolution of either the density or velocity perturbations can be de-scribed by a single second order diﬀerential equation.In the case of MG theories,this equation is simpler as the only source is provided by the Newtonian potentialψ. From Eqns.9and10we get,for the linear solution,δ( k,t)≃δinitial( k)D(k,t),¨δ+2H˙δ+k2ψ(1+η)¯ρMG a2D=0.(15)We can also use the relations given above to obtain the linear growth factors forθand the potentials from D. Note that in general the growth factors for the potentials have a diﬀerent k dependence than D.In the Appendix we give details on the linear and second order solutions and summarize quasilinear signatures of MG theories.C.Power spectraBefore we turn to large-scale structure observables,we deﬁne the power spectra of the perturbed variables.The three-dimensional power spectrum ofδ(k,z)for instance is deﬁned asδ( k,z)δ( k′,z) =(2π)3δD( k+k′)Pδ(k,z).(16) where we have switched the time variable to redshift z. The power spectra of perturbations in other quantities are deﬁned analogously.We will denote the cross-spectra of two diﬀerent variables with appropriate subscripts,for example Pδψdenotes the cross-spectrum of the densityδand the potentialψ.We write down next the relation between the power spectra of the two potentials and the density in DE and MG scenarios.From the Poisson equation(7)for GR we haveGR:Pφ(k,z)=(4πG)2a4¯ρ2GRPδ,GR(k,z)5 where Pφis the power spectrum of the potentialφ.Usingthe Friedman equation for GR the above equation is oftenwritten asGR:Pφ(k,z)=9a2k4,(18)where H0is the present day value of the Hubble param-eter,andΩis the dimensionless density parameter.The Poisson equation(12)for MG gives the following equations for the power spectra of the metric potentials. MG:Pψ+φ(k,z)=[8π˜G eﬀ(k,z)]2a4¯ρ2MG Pδ,MG(k,z)/k4or,Pφ=[8π˜G eﬀ(k,z)]2k4(19)where we have used Eqn.13to get the equation for Pφ. For LSS observables,we will need to the power spec-tra of(ψ+φ)for lensing,ofψfor dynamics,and ofδfor tracers of LSS.We will use Eqns.17-19above to connect them,along with the relations between the two potentials(Eqn.8for GR and Eqn.13for MG).With these relations we can express diﬀerent observable power spectra in terms of a single density power spectrum–for MG this will involve the functions˜G eﬀ(k,z)andη(k,z).RGE-SCALE STRUCTUREOBSER V ATIONSWe will assume that the background expansion rate is determined by a set of observations:Type Ia supernovae, baryon acoustic oscillation(BAO)and other probes at low redshift and the CMB and nucleosynthesis at high redshift.These observations measure the luminosity orangular diameter distance at a given redshift.The dis-tance measures in a spatiallyﬂat universe are,within factors of1+z,simply the comoving coordinate distance:χ(z)= z0dz′dλ2+Γµρσdxρdλ=0(21)For the metric of Eqn.1,this gives the following relation for theﬁrst order perturbation to the photon trajectory (generalizing for example from Eqn.7.72of[31]):d2x(1)µ6 deﬂection angle formula to get the shear power spectrumon angular wavenumber l([32]):Cγi γj(l)= dχW i(χ)W j(χ)k−4Pψ+φ k=lχi(25)for source galaxies at a single comoving distanceχi≡χ(z i)(it can be easily generalized for sources speciﬁed by a redshift distribution).We have assumed aﬂat back-ground geometry for simplicity;our results throughout this paper can be generalized to a curved spatial geome-try by replacingχin the argument of W by the angular diameter distance.Note that in the literature the lensing power spectra for GR are expressed in terms of the density power spec-trum Pδ(k)assuming the standard Poisson and Friedman ually anisotropic stress is neglected so that one can substitute into the above equation the relation between the power spectra:Pψ+φ=9k−4H40Ω2Pδ/a2 from Eqn.18.For MG,this substitution breaks down due to the modiﬁcations of the Poisson equation and the Friedman equation.However the correct substitution can be made in terms of˜G eﬀ(k,z)using equation19and the modiﬁed Friedman equation(which depends on the spe-ciﬁc theory).Since lensing probes the sum of the metric poten-tials,with the deﬂection angle formula following from the geodesic equation(which simply describes how cur-vature aﬀects trajectories),it may not by itself test the ﬁeld equations of the gravity theory.However lensing measurements at multiple source redshifts are sensitive to the growth of the lensing potential,which does of-fer a test of the MG theory.And by combining lensing with other observables,the relation of Pψ+φto Pδcan be tested.Recent studies that have examined constraints on MG theories with weak lensing include[18,29,33,34,35]. Another important observable in lensing is galaxy-galaxy lensing,the mean tangential shear around fore-ground(lens)galaxies.Its Fourier transform,the galaxy-lensing cross-spectrum,depends onψ+φand on the galaxy number density.It is given by an equation similar to Eqn.24,with the power spectrum of the lensing po-tential in the integrand replaced by the three-dimensional cross-power spectrum,and with one of the weight func-tions replaced by one representing the foreground galaxy distribution:C gi γj(l)= dχW gi(χ)Wγj(χ)χ,χ),(26)where W gi is the normalized(foreground)galaxy redshift distribution(e.g.[36]).Galaxy-galaxy lensing has been well measured from the SDSS survey.It is a very useful check on galaxy bias,hence it aids the interpretation of galaxy clustering measurements([37])as well.Assumptions:In using weak lensing observations withthe above formalism,one assumes that intrinsic corre-lations are negligible or removable(in general these can diﬀer for diﬀerent gravity theories),that the weak lensing approximation is valid,and that galaxy properties that aﬀect photometric redshift determination are not aﬀected by the gravity theory.Newtonian Potentialψ:This can be measured by dynamical probes,typically involving galaxy or cluster velocity measurements.If gravity is the only force deter-mining galaxy accelerations at large scales(as expected), we have from Eqn.10:k2ψ=d(aθg)HP gθg(k)+u4H2(z) (28) where u=k /k is the cosine of the angle of the k vectorwith respect to radial direction;P g,P gθg,Pθgare the real space galaxy power spectra of galaxies,galaxy-θg andθg, respectively;σv is the1D velocity dispersion;and F(x) is a smoothing function,normalized to unity at x=0, determined by the velocity probability distribution.The dependence on u enables separate measurements of all three power spectra,though Pθgis the hardest to measure with high precision[40,41].Furthermore,measurements of P s g at smaller scales provide information on pairwise velocity dispersionσv[43].In the linear regime,we can rewrite Eqn.27ask2ψ=d(aDθ)/dt7ﬂuid,we can see that the DM and DE velocities evolve diﬀerently since only the latter is aﬀected by pressure perturbations in the DE.As aﬁrst order approximation, galaxies and baryonic gas velocities trace that of the DM. So what one actually measures isθg≃θDM=θDE=θ. This distinction can be relevant for DE models with large perturbations on sub-horizon scales if these are not corre-lated with the matterﬂuctuations(i.e.if the DE power spectrum has a diﬀerent shape from the matter power spectrum).Assumptions/Caveats:The galaxy peculiar velocity only probesψwhere there are galaxies.So potentially there is a bias related to the environment of galaxies. However,since gravity is a long range force,the poten-tial where galaxies reside is determined by matter over a much larger region and thus should be unbiased with respect to the overallψ.Galaxies themselves are not suﬃciently massive to contribute to this long range po-tential.However,to obtain˙v g from limited redshift bins, one does need to parameterize the redshift dependence of v g.The accuracy of the velocity information inferred from the redshift space galaxy power spectrum relies on the modeling of the redshift distortion.The derivation of Eqn.28is quite general–it can be applied to general DE or MG models.However,Eqn.28does not describe red-shift distortions to percent level accuracy[39].Nonethe-less,with improved modeling of the correlation function in redshift space[44]the associated systematic errors in velocity(andψ)measurements can be reduced. Density contrastδ:The clustering of galaxies is one of the earliest measures of large-scale structure,and its measurements have advanced over the last three decades. The galaxy power spectrum P g is the simplest statistical measure of correlations in the galaxy number density. Several other probes of large-scale structure also probe the densityﬁeld:clustering of the Lyman-alpha forest, clustering of quasars and galaxy clusters,the abundance of galaxy clusters,and(in the future)21-cm emission measurements of the high-redshift universe. However,given a measured galaxy power spectrum, the power spectrum Pδof the underlying mass densityδmay diﬀer due to galaxy bias.Further the galaxy-density relation may be non-local and vary slightly in diﬀerent gravity theories due to diﬀerences in the tidalﬁeld that inﬂuence collapsed objects such as galaxy halos.We will restrict ourselves to large scales(k≪k nl,the nonlinear wavenumber)where bias is scale independent in simple models of galaxy formation.This allows us to infer the mass power spectrum from the galaxy power spectrum without detailed modeling of their relation,because it is possible toﬁt for the bias directly from the data.We discuss below the caveats to this assumption for clustered dark energy.The galaxy density in three-dimensional space may be expressed in terms of the density and bias parameters b1and b2asδg≡δn g2δ2.(30)This expansion is useful for small values ofδ;it can be used in a perturbative expansion to explore what mea-surements are suﬃcient to measure the bias parameters b1,b1as well asδ(see[45]for details on the bias formal-ism).Eqn.28above shows how the three-dimensional galaxy power spectrum P g can be obtained from redshift space measurements.A second way of measuring P g is from imaging data with photometric redshifts.This pro-vides measurements of the angular power spectrum of galaxies,which is a projection of the three-dimensional galaxy power spectrumC g(l)= dχW2g(χ)χ,χ ,(31)where W g is the normalized redshift distribution of galax-ies included in the sample.With good photo-z’s it is a narrow range with width of order0.1in redshift,so that many such angular spectra can be measured at diﬀerent mean redshifts from a survey(e.g.[46]).1.Galaxy bias with clustered dark energyIn clustered dark energy models it is not a priori clear whether the galaxy overdensity is related to the matter overdensityδm or to the totalﬂuid overdensityδGR.We argue below that at least for some galaxy populations,δg is directly related toδm,even though the evolution of the matter density responds to the full gravitational potential(which receives contributions from dark energy clustering as well).One way to see this is to consider the centers of mass of galaxy halos at suﬃciently high redshift z i that the dark energy density is negligible.The clustering of these halo centers is then simply a biased version of the mass distribution.Hence at z i one can writeδg(z i)=b(z i)δM, with b(z i)independent of scale for large enough scales. As they evolve to redshifts below unity,their motions are given by the potentialψ,just as for the matter ﬁeld.Hence their evolution obeys the continuity and Eu-ler equations:˙δg≃−θg/a and˙θg≃−Hθg+k2ψ/a. The matter density obeys the same equations withδM andθM as the density and velocity perturbations.This means that the bias factor preserves its scale indepen-dence:at low redshift,it relates the galaxy power spec-trum to the matter power spectrum and is not directly sensitive to the clustering of dark energy.For example the halo model expression[47,48]for the bias evolu-tion is:b(z)≃1+(ν−1)/δsc(z)whereδsc(z)∝D(z) is the density required for spherical collapse at z,and ν≡δsc(z)/σwithσthe smoothed rms massﬂuctuation. The expression for ellipsoidal collapse has two additional parameters but still has no scale dependence.8 Clustered dark energy follow Eq.6with w=0andσ=0,so it has a diﬀerent time and spatial dependencefromδm.If the dark energy clusters signiﬁcantly,it istherefore possible that galaxies have a scale dependentbias relative to it and therefore to the total densityﬁeld.The above argument is very general but relies on someapproximations.These are well justiﬁed for massive ha-los,for which the evolution at low redshift is very sim-ple:consider galaxy halos of mass M≫M∗,where M∗is the standard halo model nonlinear mass.The centersof mass of these halos can be mapped to high-σpeaks inthe nearly Gaussian mass distribution at high redshift.Moreover,they do not move signiﬁcantly,so it is evidentthat their power spectrum at large scales evolves simplyby the growth of its amplitude.Such massive halos corre-spond to galaxy clusters and LRG’s at moderate to highredshift.For galaxies in lower mass halos,halo motionsand mergers change their clustering at low redshift,soone has to be careful in modeling their bias factors.Another route toδin any GR scenarios is through themetric potentials.Given lensing measurements ofψ+φand dynamical measurements ofψ,one can obtain thepotentialφ.Using this,the Poisson equation(7)thengivesδ,since the Gravitational constant is known in GR.Thusδis not independent of the metric potentials evenfor clustered DE models.2.Empirical determination of biasTo leading order then,knowledge of b1allows us torelate P g to Pδ.Barring extreme scenarios of clustereddark energy,we takeδto be the full densityﬁeld.Provided a halo-model description applies reasonablywell to our universe,bias can be determined by combin-ing observations and using two and three-point statistics.For concreteness we consider the bias parameters b1,b2that can be determined from the data using the powerspectrum and bispectrum(denoted B)measurements.Ina deterministic bias model,one can then get the densitypower spectrum.With P g=b21Pδand the reduced three-point parameter Q∼B/P2(see the Appendix and[45]for full expressions),one has a relationship between theQ parameter of galaxies and mass[49,50]:Q g=Qδb21,(32)By using P g and measurements of Q g for diﬀerent tri-angles,both bias parameters and Pδcan be determined.(A similar analysis can be done in real space,ing counts in cells.The skewness S3is given by the shape of the power spectrum and bias parameters.)While this is a simpliﬁed model,it helps us address what changes for MG:the predictions for Pδand Qδboth change,with the former given by the new linear growth factor on large scales and the latter by next order terms in perturbation theory(see the Appendix for more details).For well spec-iﬁed gravity scenarios,these calculations can be done and thus the bias factors determined from measurements.A second approach to measuring b1is to use the galaxy-mass cross-correlation measured by galaxy-galaxy lens-ing in combination with the galaxy power spectrum(e.g.[37]).This has the advantage that one uses only two-point statistics that can be measured with high accuracy. However,as discussed below and by[25],for MG theo-ries there is a complication because the Poisson equation is needed as well since lensing measures the potentials rather thanδ.So for MG theories,the extraction of the bias parameter in this approach is more complicated–but nevertheless feasible by jointlyﬁtting for bias and ˜Geﬀ.3.Galaxy cluster mass functionA diﬀerent probe ofδis provided by the mass func-tion of galaxy clusters.Given Gaussian initial conditions and a spherical/ellipsoidal collapse model,the number density of galaxy clusters can be related to the linear density contrast.In the spherical collapse scenario,a re-gion containing mass M will collapse if the overall density ﬂuctuation exceeds a thresholdδc.The number of such regions can be predicted from the Gaussian statistics and thisﬁxes the halo mass function dn/dM,the number of halos with mass M.In the standardΛCDM cosmology,gravitational dy-namics is determined by GR.The mass function of galaxy clusters is sensitive to the smoothed mass density vari-anceσ2R on scale R,which is dependent on the cluster mass and is typically of order10Mpc(e.g.[51]).This is related to the density power spectrum as:σ2R= d3k。

高一年级英语宇宙探索与科学发现单选题40题

高一年级英语宇宙探索与科学发现单选题40题1. The ______ is a huge system of stars, gas, and dust held together by gravity.A. planetB. galaxyC. moonD. comet答案：B。

解析：本题考查宇宙概念中的星系相关词汇。

A选项“planet”意为行星，行星是围绕恒星运转的天体，并非由恒星、气体和尘埃组成的巨大系统，所以A选项错误。

B选项“galaxy”是星系的意思，星系是由恒星、气体、尘埃等物质通过引力聚集在一起的巨大系统，符合题意，所以B选项正确。

C选项“moon”是月亮、卫星的意思，卫星是围绕行星运转的天体，与题干描述不符，C选项错误。

D 选项“comet”是彗星的意思，彗星是在太阳系中运行的一种天体，与题干描述的巨大系统不符，D选项错误。

2. Which of the following is the largest in the solar system?A. EarthB. JupiterC. MarsD. Venus答案：B。

解析：本题考查太阳系中的星球大小比较相关知识及词汇。

A选项“Earth”是地球，地球在太阳系中不是最大的星球。

B选项“Jupiter”是木星，木星是太阳系中最大的行星，所以B选项正确。

C选项“Mars”是火星，火星比木星小，C选项错误。

D选项“Venus”是金星，金星也比木星小，D选项错误。

3. A ______ is a group of stars that form a pattern in the sky.A. constellationB. nebulaC. asteroidD. meteor答案：A。

解析：本题考查星座的概念相关词汇。

A选项“constellation”是星座的意思，星座是天空中一群组成特定图案的恒星，符合题意，A选项正确。

B选项“nebula”是星云的意思，星云是由气体和尘埃组成的云雾状天体，与星座概念不同，B选项错误。

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a rXiv:g r-qc/2575v 219Aug22A Machian Model of Dark Energy R.G.Vishwakarma Inter-University Centre for Astronomy &Astrophysics,Post Bag 4,Ganeshkhind,Pune 411007,India E-mail:vishwa@iucaa.ernet.in Abstract Einstein believed that Mach’s principle should play a major role in ﬁnding a meaningful spacetime geometry,though it was discovered later that his ﬁeld equations gave some solutions which were not Machian.It is shown,in this essay,that the kinematical Λmod-els,which are invoked to solve the cosmological constant problem,are in fact consistent with Mach’s ideas.One particular model in this category is described which results from the microstructure of space-time and seems to explain the current observations successfully and also has some beneﬁts over the conventional models.This forces one to think whether the Mach’s ideas and the cosmological constant are interrelated in some way.KEY WORDS:Mach’s principle;cosmological constant;dark energyReceived an Honorable mention in the Essay Contest −2002sponsored by the Gravity Research Foundation .1When Einstein introduced the cosmological constantΛinto hisﬁeld equa-tions to obtain a static solution,he was guided by Mach’s principle,which argued that the distribution of matter determined the precise geometricalnature of spacetime and hence forbade the notion of empty universe.He be-lieved that the presence of matter was essential for a meaningful spacetime geometry[1].However,he had to discount his idea when deSitter discovereda cosmological model withΛand no matter at all which had both static and dynamic ter he also dismissedΛwhen it was foundthat the universe was expanding.One however notices that if a dynamicΛ(t)is introduced into Einsein’sﬁeld equations,no solution is possible in the absence of matter.This is clear from the divergence of theﬁeld equations: [R ij−18πG g ij ;j.(1) (I shall use the units with c=1throughout.However,c will be restoredwhenever needed.)Obviously a solution with a dynamicΛis possible onlyif T ij=0(and T ij;j=0).In the absence of matter(or even if the matter is conserved),Λhas got to remain a constant.Thus the empty spacetime cannot be obtained as a solution of general relativity with a dynamicΛ(t).This way of introducingΛinto Einstein’s equations gives it a status ofa source term.Now it(Λ/8πG)represents the energy density of‘emptiness’(vacuum)and hence invites particle physics to interact with general relativity viaΛ.Note that the only possible covariant form for the energy momentum tensor of the quantum vacuum is T ij v=−ρv g ij,which is equivalent to the cosmological constant.It behaves like a perfectﬂuid with the energy density ρv=Λ/8πG and an isotropic pressure p v=−ρv=−Λ/8πG.The conserved quantity is now the sum of matter and vacuum(and not the two separately), as is obvious from equation(1).Here comes the problem:the value of vacuum energy at the Planck epochcomes out as≈1076GeV4,which is123orders of magnitude larger than its value predicted by the Friedmann equation˙S2S2=8πG3,(2)which givesΛ0≈H20or equivalentlyρv0≈10−47GeV4[2].(The subscript ‘0’denotes the value of the quantity at the present epoch.)It is fortunate for2general relativity that this predicted value ofΛby the theory is also consis-tent with the recent observations of type Ia supernovae[3]and the anisotropy measurements of the cosmic microwave background radiation(CMBR)[4],taken together with the complimentary observational constraints on matterdensity[5];all indicate that the present constituent of the universe is domi-nated by some weird kind of energy with negative pressure,commonly knownas‘dark energy’.The simplest candidate for dark energy is the cosmologi-cal constant,though plagued with this so called the cosmological constantproblem.Obviously the problem arises due to the incompatibility of general relativity and particle physics.The dynamicalΛwas,in fact,invoked in an attempt(phenomenological in nature)to solve this problem(historically,itwas not invoked to make the solutions of Einsein’s equations consistent with Mach’s ideas).The rationale behind this approach is thatΛwas large duringthe early epochs and it decayed as the universe evolved,reducing to a smallvalue at the present epoch.There is another phenomenological approach to solve this problem,whichhas become very popular since recent observations suggested the existenceof a nonzeroΛ.This invokes a slowly rolling down scalarﬁeldφ,commonly known as‘quintessence’,with an appropriate potential V(φ)to explain theobservations[6].Note that though the quintessenceﬁelds also acquire negative pressureduring the matter dominated phase and behave like dynamicalΛ(withΛeﬀective≡8πGρφ),they are in general fundamentally diﬀerent from the dy-namical(kinematical)Λ.In the former case,quintessence and matterﬁeldsare assumed to be conserved separately(through the assumption of minimal coupling of the scalarﬁeld with the matterﬁelds).However,in the latter case,the conserved quantity is[T ij+T ij v],as have been mentioned earlier. This implies that there is a continuous creation of matter from the decaying Λas is clear from the following.ρ=CS−3(1+ω)−S−3(1+ω)possible toﬁnd a V(φ)which explains the observations,as has been shown recently by Padmanabhan[7].This result is irrespective of what the future observations reveal about the given S(t)andρ(t),and hence makes these models trivial.Like the anthropic principle[8],these models also don’t have any predictive power and lead to similar late time behaviour of the universe.The true solution of the cosmological constant problem should be pro-vided by a full theory of quantum cosmology,which is unfortunately not available at the moment.However,some arguments have been made,based on the quantum gravitational uncertainty principle and the discrete structure of spacetime at Planck length,which have made it possible to connect the cosmological constant with the microstructure of spacetime[7,9].By assum-ing thatΛis a stochastic variable arising from the quantumﬂuctuations and it is the rmsﬂuctuation which is being observed in the cosmological context, it has been shown that the uncertainty in the value ofΛcan be written as∆Λ=1,(4)where0is the four volume of the universe.If one estimates the‘radius’of the universe by S≈ct≈cH−1,then this reduces to∆Λ≈H2,(in units with c=1),(5) which matches exactly with the present observations.There are also other ways which suggestΛ∝H2.Two such ways have been described in the following(two more have been described by Padman-abhan in his paper[7]).(i)We know that a positiveΛintroduces a force of repulsion between two bodies which increases in proportion to the distance between them.This force experienced by a test particle at the scale of the whole universe is cΛH−1.If this repulsive force roughly balances the gravitational attraction 4πGcρ/3H of the universe on the test particle,oneﬁndsΛ≈H2,provided Ωm(≡8πGρ/3H2)is of order unity.(ii)From the dimensional considerations,it is always possible to writeΛin terms of Planck energy density times a dimensionless quantity[10]:Λ≈8πGρPl t Pl t H α,(6)4where t Pl≡(G¯h/c5)1/2and t H≡H−1are the Planck and Hubble times respectively andρPl≡c5/G2¯h is the Planck energy density.Forα=2, which gives the right value ofΛat the present epoch,equation(6)leads to Λ≈H2.By writing this law asΛ=nH2,where n is a constant parameter,the dynamics of the resulting model can be obtained,from equations(2)and(3), asρ∝Λ∝H2∝t−2,S∝t2/[(3−n)(1+ω)],n<3,(7) where we have considered k=0,as has been suggested by the recent CMBR observations[4].The cases n≥3(whereρ≤0)are either unphysical or not compatible withΛ=Λ(t).Note that the ansatzΛ=nH2is equivalent to assuming thatΩΛ(≡Λ/3H2=n/3)is a constant and,hence,so isΩm (=1−n/3)in aﬂat model.Henceρv/(ρ+ρv)=n/3is also a constant.The deceleration parameter,in the model,is obtained as(3−n)(1+ω)q=0according as n<<Interestingly these constraints are also consistent with the CMBR anisotropy observations which,especially theﬁrst peak in the angular power spectrum curve which has been conﬁrmed by various observations,require n to change at a redshift of a few.Thus if the expansion dynamics switches over from deceleration to acceleration at z=z1,the angular diameter distance to the last scattering surface(at z=z dec)is given byd A=1H(n2;z)+ z dec z1dzH0(1+z dec) z10(1+z)(n2−3)/2dz+ z dec z1(1+z)(n1−3)/2dz .(10)If one considers n2=1.5(from the SN and the radio sources data)and z1=5(to be on the safe side in view of the future higher redshift observations), then a value of n1=0.15gives the angle subtended by the Hubble radiusd H(z dec,n1)(with z dec=1100)at the observer as≈0.90which is equivalent to a peak at a Legendre multipole sizeℓ≈200.This is exactly what the CMBR anisotropy observations have measured.Note that the parameterspace(n1,z1)is wide enough which makes the model robust.Another attractive feature of the model is that it supplies a suﬃciently large age of the universe,which is very remarkable in view of the fact that theage of the universe in the FRW model with a constantΛis uncomfortably close to the age of the globular clusters t GC=12.5±1.2Gyr[15].Thequintessential models give even lower age.In Figure1,we have plotted the expansion age of the universe t0as a function ofΩΛ0in the present model, together with the favoured quintessence model(ωφ≡pφ/ρφ=−0.8)and the FRW model with a constantΛ(ωφ=−1).Note that if the required mass densityΩm0of the universe was smaller,one could get higher age in thesemodels,as is clear from theﬁgure.This does not,however,seem likely,as the recent measurements give very narrow range ofΩm0asΩm0=0.330±0.035 at one sigma level[5].By using H0=72±7km s−1Mpc−1(which is recently measured by the Hubble Space Telescope key project and is also consistent with a host of other experiments[16]),this value ofΩm0gives t0=12.7±1.6 Gyr in the FRW model with a constantΛ.This is roughly consistent with the60.20.40.60.8010121416182022A g e i n G y r H 2constΩΦ 0.8Figure 1:The age of the universe is plotted as a function of ΩΛ0in some ﬂat models,by using H 0=72km s −1Mpc −1.The horizontal dotted line represents the age of the globular clusters t GC =12.5Gyr.The vertical dotted line corresponds to the mass density of the present universe (Ωm0=0.33).7value t0=14±0.5Gyr estimated from the CMBR observations,which has been claimed to give more accurate age of the universe[17].The value of t0in the favoured quintessence model is obtained as t0=12.3±1.5Gyr,which seems in real trouble in view of t GC=12.5±1.2Gyr.In this connection it is very encouraging that the modelΛ∝H2,where the expression for the ageof the universe yields t0≈2/(3Ωm)H−10,gives t0≈27.4±5.6Gyr which is remarkably high.In light of the successes and achievements stated above of this model, one is inclined to ask if it is just a matter of coincidence that the model is consistent with Mach’s ideas and at the same time it solves the cosmological constant problem(at least phenomenologically).Should Mach’s principle play some fundamental role in solving the cosmological constant problem? Two concepts(Mach’s principle and the cosmological constant),invoked by Einstein,and later dismissed by himself,seem to be unavoidable.Are they really interlinked in some intricate way?Only the future will answer these questions.ACKNOWLEDGEMENTSThe author thanks Professor J.V.Narlikar for useful discussion and the Department of Atomic Energy,India for support of the Homi Bhabha post-doctoral fellowship.REFERENCES:[1]Narlikar J.V.(2002),An Introduction to Cosmology,Cambridge Univ. 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