Standard cosmological model & dark energy. Atsushi Taruya Research Center for the Early Universe, Univ.Tokyo

Transcription

1 月 日 月 日 手 Standard cosmological model & dark energy Atsushi Taruya Research Center for the Early Universe, Univ.Tokyo

2 Aim of this talk A quick overview of modern cosmology brief summary of cosmological physics concordant cosmological model: issues & prospects For further study,

3 Contents Cosmology: fact sheets Designing the observed Universe Standard cosmological model Dark energy Future prospects: toward precision cosmology

4 Ultimate goal of cosmology Cosmology Understanding of the nature of the Universe Birth and evolution of the Universe Matter content of the Universe {Origin of structure of the Universe Starting point A consistent picture to explain the observed properties of the Universe based on theory and cosmological observations { minimal

5 Fact sheets (1) Universe is expanding Hubble law { v = Hd E.Hubble v: galaxy recession velocity d: distance between galaxy and observer Universe started with hot plasma (Big-Bang): Nucleosynthesis Light-element abundance D, 3 He, 4 He, 7 Li G.Gamov Photon decoupling from thermal bath Cosmic Microwave Background (CMB)

6 Fact sheets (2) Universe is basically homogeneous, but there exists (small) inhomogeneities CMB T=2.73K contrast 104 Galaxy distribution 2dF GRS APM survey 30deg. slice 2 deg. slice

7 Fact sheets (3) Observed inhomogeneities are apparently random, but have statistically regular nature CMB T (θ, φ) =,m a m Y m (θ, φ) galaxies n gal (x) n gal 1= d 3 x δ( k) e i k x C = m= a m 2 ; P (k) = 1 (2π) 3 k =k δ( k) 2

8 Designing the observed Universe Basic ingredients Dynamics of cosmic expansion thermal history of the Universe (hot Big-Bang) Structure formation large-scale structure (LSS) in CMB & galaxy distribution To understand these, we need both microphysics and macro-physics

9 Underlying physics (1) Standard assumptions Dynamics of cosmic expansion: general relativity under the cosmological principle Evolution of inhomogeneities: (homogeneous & isotropic) general-relativistic perturbation theory coupled with non-equilibrium transport processes Key word Gravity microphysics

10 Underlying physics (2) Friedman equation basic eq. that describes cosmic expansion scale factor a is dynamical variable Einstein eq. with Robertson-Walker metric ( size of the Universe) : Hubble parameter at present density parameter of mass a=1 implies present time curvature parameter

11 Underlying physics (3) Minimal set of eqs. that account for inhomogeneities (CMB & LSS): Cosmological perturbation (general-relativistic linear perturbation) Relativistic Boltzmann eqs.+ Ionization rate eq. Main species (massless) Neutrinos Non-baryonic matter (cold dark matter, CDM) Gravity Photons Baryons Thomson scatt. (electron) CMB LSS

12 Basic picture (1) Microphysics Thomson scattering Electromagnetic interaction between the recombination and decoupling time CMB photon Nucleon electron Last scattering surface First objects galaxies beginning 380,000 1billion 10 billion today (year)

13 Basic picture (2) Macro-physics Evolution of super-horizon scale fluctuations based on general relativity Physical length Quantum fluc. Last scattering surface inflation radiation era matter era time

14 Basic equations : summary Friedman eq. H 2 = H 2 0 (1 + z) 3 Ω m + (1 + z) 4 Ω r + (1 + z) 3(1+w) Ω DE Cosmological perturbation coupled with Boltzmann eqs. Assuming flat universe ( Ω K =0) Φ(k), Ψ(k) : gravitational potential & curvature perturbation Θ(k, µ) : (photon) temperature fluc. N (k, µ) : neutrino fluc. (massless) δ b (k), v b (k) : baryon density & velocity fluc. δ(k), v(k) : CDM density & velocity fluc.

15 Relation with Observables Solutions of these eqs. can be translated to observables: LSS Matter power spectrum CMB Angular power spectrum of temperature anisotropies P (k) =P init (k) δ m (k; η 0 ) δ m (k; η init ) primordial matter spectrum C = 2 π There are several publicly available code to solve these eqs.: CMBfast, CAMB, CMBEASY,... 0 dk k 2 P init (k) Θ (k; η 0 ) δ m (k; η init ) 2 δ m Ω c Ω m δ c + Ω b Ω m δ b + Ω ν Ω m δ ν 2

16 Model parameters There are a number of model parameters to be specified Initial conditions (adiabatic) Cosmic expansions Others A s n s α s scalar amplitude scalar spectral index scalar running index density parameters curvature parameter Hubble parameter reionization optical depth r tensor-to-scalar ratio n t tensor spectral index = A t A s # of parameters further increases if we consider isocurvature fluc. Ω c, Ω b, Ω ν, Ω DE Ω K h = H 0 /(100km/Mpc) τ P init (k) dark energy E.O.S w There exist other nuisance parameters such as galaxy bias

17 Minimal model Adiabatic power-law & no tensor contribution α s = r = n t =0 Flat cosmology, massless neutrinos, cosmological const. Ω K = Ω ν =0,w= 1 A s scalar amplitude Note-. In total, 6 parameters n s Ω c Ω b scalar spectral index density parameter of CDM density parameter of baryon Ω DE =1 Ω c Ω b h Hubble parameter τ reionization optical depth

18 Parameter dependence: CMB τ smear overall shape Ω b h 2 n s A s Ω m h 2

19 Parameter dependence: LSS k n s Baryon acoustic oscillation oscil. amplitude Ω b /Ω m k n s 4 A s k eq Ω m h

20 Latest results Large-scale structure CMB Luminous red galaxies N gal 110, 000 SDSS DR7 V survey =0.26 (h 1 Gpc) 3 7, 900deg 2 WMAP5 Komatsu et al. (2009) Reid et al. (2009) In addition, distance-redshift measurement from distant supernova observation is used

21 Results of parameters KOMATSU ET AL. KOMATSU ET V WMAP5 + SDSS DR7 lass Parameter parameter WMAPΛCDM 5YearML a Class WMAP+BAO+SNParameter ML WMAP 5YearMean 5YearML ba WMAP+BAO+SN M rimary 100Ω b h Ω Primary Ω ± m ± b h Ω c h Ω c h ± ± Ω Λ H ± Ω Λ ± ± n s D V (0.35) ± n s ± τr s /D V (0.35) ± τ ± ± R (kc Ω0 ) 2.41 k R (kc 0 ) ( ± 0.11) ( ± ) 9 erived σ 8 w Derived σ ± ± H kms Ω Λ Mpc ± kms 1 Mpc 1 Komatsu H s ± 1.3 km s 0 et 72.4kms al. (2009) 1 Mpc kms 1 Mpc Ω b Ω b ± ± Ω c Age (Gyr) ± Ω c ApJ.Suppl. 180, ± ± Ω m Ωh 2 tot Ω ± m h Ω b h zreion d ± z 11.0 ± ± 1.4 t0 e reion d Ω c h Gyr Gyr t A 0 e s ± 0.13 Gyr Gyr Gyr ± τ ± n otes. Notes. s 0.96 Dunkley et al. (2009). n ML s refers ± ln(10 10 to the Maximum A 05 ) Likelihood parameters. a Dunkley et al. (2009). ML refers Ω to the Maximum Likelihood parameters. Dunkley et al. (2009). Mean refers to the mean of the posterior b distribution Dunkley etof al. each (2009). parameter. Mean refers c 0.24 to the mean of the posterior distribution of each pa k 0 = Mpc 1. 2 R σ (k) 8 = k3 P R (k)/(2π ) (Equation ± (15)). c k 0 = Mpc 1. 2 R (k) = Ω k3 P R b (k)/(2π ) (Equation (15)). Redshift of reionization, if the universe was reionized instantaneously d Redshift fromof thereionization, neutral state if tothe universe fully ionized was reionized state at z reion instantaneously. from the neutra The present-day age of the universe. e The present-day age of the universe. Reid et al. (2009) Table 1 Table 1 Summary of the Cosmological Parameters of ΛCDM Model and thesummary Corresponding of the Cosmological 68% Intervals Parameters of ΛCDM M arxiv: c.f. WMAP5 only h 0.69 τ 0.08 Table 2 Table 2 Summary of the 95% Confidence Limits on Deviations from the Simple Summary (Flat, of Gaussian, the 95% Adiabatic, ConfidencePower-Law) Limits Deviations ΛCDM Model from the Simpl

22 Note Extension of parameter set does not significantly change the results spectral running curvature neutrino masses tensor contribution... Minimal 6-parameter model is currently the best standard cosmological model that explains all the observations

23 From WMAP papers, 8. CONCLUSIONS Spergel et al. (2003) Cosmology now has a standard model: a flat universe composed of matter, baryons, and vacuum energy with a nearly scale-invariant spectrum of primordial fluctuations. In this cosmological model, the properties of the universe Spergel et al. (2007) are characterized by the density of baryons, matter, and the expansion rate: b, m ; and h. FortheanalysisofCMB 9. CONCLUSIONS results, all of the effects of star formation can be incorporated in a single number: the optical depth due to reioniza- The standard model of cosmology has survived another rigorous set of tests. The errors on the WMAP data at large l are now tion,. The primordial fluctuations in this model are 3 times smaller, and there have been significant improvements in characterized by a spectral index. Despite its simplicity, it is other cosmological measurements. Despite the overwhelming an adequate fit not only to the WMAP temperature and force of the data, the model continues to thrive. This was the basic polarization data but also to small-scale CMB data, largescale structure data, and supernova data. This model is con- result of Spergel et al. (2003) and was reinforced by subsequent analyses of the first-year WMAP data with the SDSS (Tegmark sistent with the baryon/photon ratio inferred from observations of D/H in distant quasars, the HST Key Project 7. CONCLUSION et al. 2004a) and analysis of first-year WMAP plus the final 2dFGRS survey (Sanchez et al. 2006). After the analyses in this paper were completed, a larger With SDSS 5-years LRG sample of integration, was released. the WMAP temperature and polarization data have improved significantly. An improved determination of the third.. acoustic.... peak has enabled us to From these studies, we conclude that we have not detected any convincing deviations from the simplest six-parameter ΛCDM model at the level greater than 99% CL. By combining WMAP data with the distance information from BAO and SN, we have Komatsu et al. (2007) improved the accuracy of the derived cosmological parameters. As the distance information provides strong constraints on the

24 Cosmic pie Energy composition of the Universe today The Universe is occupied with unknown components, dark energy and dark matter Are you really happy about that?

25 WMAP papers, again Cosmology is now in a similar stage in its intellectual development to particle physics three decades ago when particle physicists converged on the current standard model. The standard model of particle physics fits a wide range of data but does not answer many fundamental questions: What is the origin of mass? Why is there more than one family? etc. Similarly, the standard cosmological model has many deep open questions: What is the dark energy? What is the dark matter? What is the physical model behind inflation (or something like inflation)? Over the past three decades, precision tests have confirmed the standard model of particle physics and searched for distinctive signatures of the natural extension of the standard model: supersymmetry. Over the coming years, improving CMB, large-scale structure, lensing, and supernova data will provide ever more rigorous tests of the cosmological standard model and search for new physics beyond the standard model. Spergel et al. (2003)

26 To do list Beyond standard model Clarifying the nature of dark energy Constraining early-universe physics Adiabaticity of initial condition Non-Gaussianity of primordial fluctuations Evidence of spectral running Detection of non-zero tensor mode Test of hypothetical assumptions General relativity on cosmological scales Constraining particle physics Detection of non-zero neutrino mass

27 Cosmic acceleration Sizable amount of dark energy implies that the Universe just started an accelerated expansion!"#$%&'() $*+) Since ρ m > ρ DE ρ = ρ m + ρ DE P P DE ρ DE Acceleration!

28 Evidence of cosmic acceleration First confirmed by distant-supernova observations 10 years ago Scale of the Universe scale factor: a Obs. of distant type-ia SNe Accelerate Decelerate Redshift: z (=1/a 1) We are living in the second phase of cosmic inflation?!

29 Nature of dark energy (1) Cosmological constant First invented by Einstein in 1917 Vacuum energy equivalent to P DE = ρ DE = Dynamical scalar field Lagrangian density L = 1 2 φ 2 V (φ) effective eq. of state Fine-tuning problem,... P φ = w(t) ρ φ Λ M 4 pl Λ 8π G Un-naturally small!! ; w(t) = φ/2 V (φ) φ/2+v (φ) < 1 3

30 Alternative possibilities As alternative explanation to cosmic acceleration, we may abandon the standard model assumptions Modification to general relativity Hidden gravity sector that modifies Friedman eq. self-accelerating universe e.g., Dvali-Gabadadze-Poratti model f(r) gravity Violation of cosmological principle We are accidentally living at the center of low-density void Late-time cosmic acceleration is apparently observed Low-density void Einstein-de Sitter

31 Current status There are currently no natural & consistent explanations Nevertheless, We cannot immediately reject/exclude these possibilities at the level of current precision Primary goal w0 : ~few % wa : ~10 % Cosmological constant or not

32 Executive reports Albrecht et al. astro-ph/ We strongly recommend that there be an aggressive program to explore dark energy as fully as possible, Peacock et al. astro-ph/ , studies of dark energy and inflation are of the utmost interest to the science community well beyond astrophysics.

33 Future missions for dark energy DETF categories Stage 1 Current status Stage 2 On-going project (~2008) WMAP, SCP, 2dF, SDSS-LRG, SDSS-II, CFHT-SNLS, CFHTLS,... Improvement factor normalized by stage 2 including CMB prior 1 Stage 3 Near-term project (~2014+) DES, Pan-STARRS4, SuMIRe, BOSS ~ 3 Stage 4 Long-term project (~2020+) LSST, JDEM, SKA space ~ 10

34 Observational techniques Precision measurement of { cosmic expansion history growth of structure Name Observation Main probe Galaxy cluster Light curves of distant supernovae Distortions of each galaxy image Spatial patterns of galaxy distribution Evolution of number density of clusters Photo-z Photo-z Spec-z SZ / WL / X-ray Combination of different techniques is quite essential

35 SuMIRe Subaru Measurement of Imaging and Redshift New instruments mounted on Subaru 8.2m telescope: Hyper Suprime-Cam (HSC) 1.5 deg^2 FOV wide-field CCD camera Prime Focus Spectrograph (PFS) 3,000 multi-fiber spectrograph { Imaging survey Weak lensing measurement Spectroscopic survey Baryon acoustic oscillations The project has been approved by the Council for Science and Technology Policy (P.I. H. Murayama, IPMU)

36 Toward precision cosmology All the signals or features indicating beyondstandard model are basically very weak Key ingredients: { Precision measurements large samples & huge observational volume reducing statistical errors and unknown systematics Precision theoretical calculations including various systematic effects ignored currently Synergy of theory and observation is really demanding

37 Summary Cosmology has a minimum standard model that accounts for the observed Universe Cosmic expansion Thermal history Structure formation But still, our understanding of the Universe is lacking : { Physical Nature of dark energy / cosmic acceleration Origin of inhomogeneities model of early universe (inflation) Next-generation precision cosmology will find an important clue to resolve these issues

38 Appendix

39 Baryon acoustic oscillation (BAO) Acoustic signature of primeval baryon-photon fluid just before the time of photon decoupling imprinted on galaxy power spectrum Characteristic scale of BAO, determined by sound horizon at decoupling time, provides a robust & unique measure. r s 110h 1 Mpc Cosmic standard ruler to measure the distance-redshift relation for high-z galaxies

40 Observation of BAO SDSS LRG sample Eisenstein et al. (2005) Percival et al. (2007)

41 BAO as standard ruler Using BAO scale as standard ruler, cosmological distance of high-z objects can be measured Angular diameter distance Redshift z z=1080 From R.C.Nichol In addition, Hubble parameter of distant objects, H(z), can be measured through Alcock & Paczynski effect.

42 ror on w is 10%, and that from curvature is below 1% unless smology is rather non-standard. Hence our result is still limy the SDSS-II BAO data volume and not by our knowledge other cosmological parameters in Eq. (16). Of course, these sions only hold for mild perturbations from the concordance logy; for other cases, one should return to the raw distance aints. We note that these expressions have not used theanguustic scale in the CMB, so they are independent of what is ning with dark energy at z>0.35. ig. 5 shows the BAO constraints from Eq. (13) on Ω m and r ΛCDM cosmologies (upper panel), and on Ω m and w for odels where constant w 1 is allowed (lower panel). ke a Gaussian prior of Ω m h 2 = ± and asthat the error on Ω b h 2 is negligible as the WMAP5 data alconstrain it to 0.5% (Komatsu et al. 2009). These constraints e the angular acoustic scale in the CMB, so they are indent of the dark energy behaviour at the redshifts beyond mple. For comparison we plot the full WMAP5 constraints atsu et al. 2009), which include the constraints on the distance scattering, and constraints from the Union supernova sample lski et al. 2008), which constrain angular diameter distance up to z 1. Results from full likelihood fits combining these re presented in Section 9. Constraints on dark energy w = P/ρ : dark energy equation-of-state parameter (w= 1: cosmological const.) BAO BAO STING THE ROBUSTNESS OF THE RESULTS he effect of redshift-space distortions ve fitted our spline BAO model to the observed SDSS power spectrum, as calculated by Reid et al. (2009), where laxy power spectrum and derived cosmological constraints esented. Using numerical simulations, a scheme is presented Percival et al. (2009) Figure 5. Cosmological constraints on ΛCDM cosmologies (upper

43 Angular projection Late-time ISW Late-time ISW Baryon compression Early-time ISW Fiducial model parameters: Hu & Dodelson (2002)