Precision Cosmology from Redshift-space galaxy Clustering

Transcription

1 27th June-1st July, 2011 Precision Cosmology from Redshift-space galaxy Clustering ~ Progress of high-precision template for BAOs ~ Atsushi Taruya RESearch Center for the Early Universe (RESCEU), Univ.Tokyo In collaboration with Takahiro Nishimichi, Shun Saito, Kazuhiro Yamamoto 1

2 Contents Classic method to measure the clustering anisotropies of galaxies is renewed with a great interest to clarify the nature of dark energy and to test theory of gravity. Accurate theoretical models for power spectrum have made a rapid progress, and are now available, taking fully account of the effect of clustering anisotropies. Large N-body simulations reveal a new feature of clustering anisotropies in halo catalogs, which sensitively depends on clustering bias. Only the improved model can account for this. 2

3 Introduction Lambda CDM model 4.6% 73% Standard cosmological model 23% characterized by 6 parameters today Flat universe filled with the unknowns energy contents SN Ia obs. Possible solution? { Late-time cosmic acceleration (Perlmutter et al. 99; Riess et al. 98) Dark energy: dynamical scalar field or cosmological const. Modified gravity: IR modification to general relativity 3

4 beyond Lambda CDM model Q Dark energy or Modified gravity? Nature of cosmic acceleration Test of gravity on cosmological scales Key Precision measurements of { Cosmic expansion Growth of structure Need independent and complementary probes other than CMB and SN Ia 4

5 Large-scale structure (LSS) Fundamental observable: Galaxy clustering patterns Note: weak lensing can also probe LSS 5

6 Cosmological information in LSS All information is encoded in statistical quantities: Power spectrum P(k), or correlation function ξ(r) Shape & amplitude Historical record of the primordial Universe (Initial condition & late-time evolution) Additional information coming from observational effect : { Alcock-Paczynski effect Redshift distortion effect With BAOs as standard ruler, Galaxy clustering offers unique opportunity measurements of these are now top priority in future surveys 6

7 Alcock-Paczynski (A-P) effect Alcock & Paczynski ( 79) Anisotropies caused by apparent mismatch of underlying cosmological models ( θ, z) observer r = c z/h(z) r = DA (z) θ Using BAO as standard ruler, H(z) & DA(z) can be measured simultaneously e.g., Seo & Eisenstein ( 03); Hu & Haiman ( 03); Blake & Glazebrook ( 03); Shoji et al.( 09) 7

8 Redshift distortion (RD) effect Anisotropies caused by peculiar velocity of galaxies through redshift measurements Large-scales peculiar velocity observer v z magnitude of distortion f(z) redshift space s = r + real space ( v z ) z ; a H(z) growth-rate parameter d ln D+ f (z) {Ωm (z)}γ d ln a e.g., γ 0.55 (GR), 0.68 (DGP) Linder ( 05) Measurement of f(z) offers a test of gravity on cosmological scales e.g., Linder ( 08); Guzzo et al. ( 08);Yamamoto et al. ( 08); Song & Dore ( 09); Percival & White ( 09); White, Song & Percival ( 09); Song & Percival ( 09); Blake et al. ( 11) 8

9 Revival of classic method Measuring clustering anisotropies is not a new method A-P effect Matsubara & Suto ( 96) Ballinger, Peacock & Heavens ( 96) Use global shape of power spectrum/correlation function to determine Ω Λ RD effect Hamilton ( 92) Adopt GR valid over cosmological scales to determine Ω m (learning from the past) 9

10 Complementarity Method Observable Measure SN Ia Weak lensing Clusters Light curves of distant SNe Shear field from galaxy images Number density of clusters g(z): growth factor DL(z) DA(z), g(z) DA(z), H(z), g(z) Galaxy clustering Spatial clustering of galaxies DA(z), H(z), f(z) Advantage: galaxy clustering provides a way to separately measure DA, H, & f 10

11 New ideas & innovation Through RD effect, galaxy clustering further provides statistical information of velocity field alternative probe of structure formation Reconstruction of velocity power spectrum Song & Kayo ( 10), Tang, Kayo & Takada ( 11) Coherent combination to constrain dark energy (Song 11) Alternative probe of bulk flow Song et al ( 11a,b) Improved technique to reduce noises has been developed Reducing cosmic variance McDonald & Seljak ( 09) Reducing shot noise/stochasticity Seljak et al. ( 09), Hamaus et al. ( 10) Reducing Finger-of-God damping Hikage, Takada & Spergel ( 11) 11

12 Latest results D V (z) (1 + z) 2 D A (z) 2 cz 1/3 H(z) Blake et al. arxiv: arxiv: WiggleZ++ (WiggleZ: ~150,000 galaxies) w BAO+CMB SDSS DR7 LRG (z=0.2 & 0.35) BAO WiggleZ (z=0.6) f(z) σ 8 (z) Ω M 12

13 On-going/up-coming surveys Spectroscopic surveys aiming at precision measurements of f(z) and/or H(z) & DA(z) WiggleZ BOSS HETDEX SuMIRe-PFS Big-BOSS Ground Subaru FastSound VIPERS GAMA Space WFIRST EUCLID 13

14 Theoretical challenges For fruitful science from high-precision measurements, Accurate theoretical template for power spectrum/correlation function Reducing the systematics is a big issue: is crucial and highly demanding Non-linear gravitational evolution Non-linear redshift distortions Galaxy biasing Small, but non-negligible at ~1% precision 14

15 Forward modeling approach First-principle calculations of P(k) & ξ(r) based on perturbation theory (PT) of LSS Development of improved treatment of PT Renormalized PT Crocce & Scoccimarro ( 06ab, 08) Closure theory Lagrangian resummation theory AT & Hiramatsu ( 08), AT, Nishimichi, Saito & Hiramatsu ( 09) Matsubara ( 08), Okamura, AT & Matsubara ( 11) Regularized PT Bernardeau, Crocce & Scoccimarro ( 08), Bernardeau, AT, Crocce & Scoccimarro (in prep.) For BAO scales of our interest (k<0.2~ <z<1.5), non-linear gravitational evolution is now under control 15

16 Improved PT in real space AT, Nishimichi, Saito & Hiramatsu ( 09) Power spectrum z=3 Correlation function Limitation of standard PT (1-loop) 16

17 Improved PT in real space AT, Nishimichi, Saito & Hiramatsu ( 09) Power spectrum z=3 Correlation function Limitation of standard PT (1-loop) For power spectrum, reliable range of improved PT becomes twice wider than that of standard PT 16

18 Modeling redshift distortions Definition redshift space real space s = r + (v ẑ) ah(z) ẑ ; { v : ẑ : peculiar velocity observer s line-of-sight direction Observed clustering pattern is apparently distorted. Anisotropy (2D power spectrum) P (k) P (S) (k, µ) ; µ ( k ẑ)/ k Power spectrum amplitude Enhancement Suppression Kaiser effect f(z) Finger-of-God effect (small-k) (large-k) 17

19 Redshift-space power spectrum Exact expression P (S) (k) = x = r r d 3 x e ik x e ikµ u z {δ(r) z u z (r)}{δ(r ) z u z (r )} u z =(v ẑ)/(ah) u z = u z (r) u z (r ) (Popular) streaming model e.g., Scoccimarro (2004) P (S) (k, µ) =e (kµ σ v) 2 Pδδ (k) 2 µ 2 P δθ (k)+µ 4 P θθ (k) Finger of God (non-linear) Kaiser fitting parameter (1D velocity dispersion)... still phenomenological 18

20 An improved model Low-k expansion from exact formula AT, Nishimichi & Saito ( 10) P (S) (k, µ) =e (kµfσ D v) 2 Pδδ (k) 2fµ 2 P δθ (k)+f 2 µ 4 FoG [kµfσ v ] P θθ (k) Damping func. +A(k, µ)+b(k, µ) Non-Gaussian correction Non-linear mode-coupling btw velocity & density A(k, µ) = 2 kµ d 3 p (2π) 3 p z p 2 B σ(p, k p, k) anti-phase oscillation θ(k 1 ) δ(k 2 ) µ 2 2 θ(k 2 ) δ(k 3 ) µ 2 3 θ(k 3 ) = (2π) 3 δ D (k 123 ) B σ (k 1, k 2, k 3 ) Gaussian correction d B(k, µ) =(kµ) 2 3 p F (p)f (k p) (2π) 3 F (p) p z p 2 P δθ (p) p2 z p 2 P θθ(p) small in amplitude (<1-2%) These also depend on f 19

21 Role of corrections in dark matter Improved model z=3 P (S) (k, µ) = =even P (S) (k) P (µ) P (S) (k)/p (S),no-wiggle Monopole z=1 z=3 Quadrupole z=1 AT, Nishimichi & Saito ( 10) 20

22 Role of corrections in dark matter Streaming model z=3 P (S) (k, µ) = =even P (S) (k) P (µ) P (S) (k)/p (S),no-wiggle Monopole z=1 z=3 Quadrupole z=1 1% convergence limit of N-body & improved PT in real space Even in 1% convergence limit, discrepancy manifest (few % in P0, >5% in P2) 21

23 Blind test: recovery of DA, H & f f Fiducial fiducial Improved with corrections model Streaming w/o corrections model (w/o corrections) AT, Nishimichi & Saito ( 10) Fitting to P0 & P2 of N-body data to estimate (DA, H, f) using MCMC H/H fid D A /D A,fid f H/H fid Improved model of redshift distortions correctly recovers the input values 22

24 Testing PT models against redshift-space halo clustering T. Nishimichi & AT, arxiv:

25 From dark matter to halos The improved PT model has successfully passed several tests in the case of dark matter clustering As a natural step, "Test against redshift-space halo clustering" Why halo? Physically well-defined objects easy to handle by N-body simulations Reconstruction technique for halo density field from LRG samples Annoying Finger-of-God damping is expected to be small Reid, Spergel & Bode ('09) Reid et al. ('10) 24

26 Halo clustering from N-body simulations Nishimichi & AT ('11) Large N-body simulations (Lbox=1.14Gpc/h, N=1,028^3) with 15 realizations 9 halo catalogs sampled over wide-mass z=0.35 M h,i [ , ] h 1 M Volume & number density roughly match those of SDSS DR7 LRG 25

27 b(k) Real-space clustering linear PT model prediction works very well at k<0.2 h/mpc Halo bias possesses (very) weak scale-dependence b(k) =P hm (k)/p m (k) Adopting a scale-dependent linear bias, δ h ( k)=b(k)δ m ( k) PT models are compared with simulations (--> Next slides) 26

28 Power spectrum in 2D P halo (k,k ) (b 2 + fµ 2 ) 2 P lin,no-wiggle(k) k k Line-of-sight N-body result shot-noise corrected observer Dark matter Light halos (bin1) Heavy halos (bin9) 27

29 Streaming model Dark matter Light halos (bin1) Heavy halos (bin9) Light halos (bin1) Heavy halos (bin9) N-body result Dark matter 28

30 Improved model Dark matter Light halos (bin1) Heavy halos (bin9) Light halos (bin1) Heavy halos (bin9) N-body result Dark matter 29

31 Power spectrum in 2D Dark matter improved(l) µ k k µ =1 k k µ =0 k 30

32 Power spectrum in 2D Dark matter improved(l) µ k k Light (bin1) improved(l) µ =1 k k µ =0 k 30

33 Power spectrum in 2D Dark matter improved(l) µ k k Light (bin1) improved(l) k µ =1 k µ =0 k Heavy (bin9) improved(l) 30

34 Multipole power P (S) (k, µ) = spectra =even P (S) (k) P (µ) P (S) (k)/[b(k) 2 P (S),no-wiggle Light (bin1) improved(l) P (S) (k)/p (S),no-wiggle Dark matter improved(l) ( = 0) ( = 2) P (S) (k)/[b(k) 2 P (S),no-wiggle Heavy (bin9) improved(l) 31

35 Halo mass dependence Choice of damping func. L: Lorentzian, G: Gaussian light heavy Fitted results of velocity dispersion bin1 improved(l,g) bin9 Goodness of fit 32

36 SDSS DR7 LRG samples Assuming linear scale-(in)dependent bias, monopole & quadrupole spectra fit to PT model Monopole Quadrupole-to-Monopole ratio P (S) (k)/p (S) 0 0,no-wiggle SDSSS b(k) =b 0 + b 1 k c P (S) 2 (k)/p (S) 0 (k) b(k) =b 0 + b 1 k c Saito, Nishimichi, AT & Yamamoto ( 10) in prep. 33

37 Constraints on DA, H & f f SDSS LRGs monopole & quadrupole Taruya et al (2010) k max =0.155h/Mpc b(k) = b 0 +b 1 k c constant bias Saito, Nishimichi, AT & Yamamoto ( 10) in prep. Simultaneously constrain DA, H & f from SDSS DR7 LRGs H/H fid D A /D A,fid H/H fid f H/H fid Resultant constraint on DA is rather sensitive to the galaxy bias 34

38 Summary Clustering anisotropies by AP & RD effects offer unique probe to precisely measure cosmic expansion & growth of structure Key science of galaxy surveys in the coming decade New ideas & innovations Precision power spectrum template from perturbation theory { New effect of non-linear RD amplified by galaxy/halo bias Failure of popular streaming model Impacts of precision model of RD on future measurements The understanding of galaxy bias is still crucial issue 35