redshift surveys Kazuhiro Yamamoto T. Sato (Hiroshima) G. Huetsi (UCL) 2. Redshift-space distortion

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1 Testing gravity with large galaxy redshift surveys Kazuhiro Yamamoto Hiroshima University T. Sato Hiroshima G. Huetsi UCL 1. Introduction. Redshift-space distortion 3. Measurement of quadrupole 4. Constraint from the quadrupole 5. Summary and conclusions 008 Kona Hawaii 1

2 1. Introduction Koyama s tal Modified Gravity models as alternatives to the dar energy fr gravity model, TeVeS theory, DGP model, etc. Ambitious challenges to the fundamental physics necessary to go beyond the standard model? A lot of observational projects for exploring the dar energy, WiggleZ, BOSS, WFMOS, HSC, DES, LSST, etc. e.g., tals in this conference Testing the general relativity it on the scales of cosmology

3 Measurement of the growth of the density perturbation will be the ey for testing the gravity theory. Constraint on the growth factor and the growth rate for testing the gravity theory Linder 05, Linder Cahn 07, Amendola, Kunz, Supone 07 Heavens, Kitching, Verde 07, Maartens, Koyama 06, Jain, Zhang 07,. Nesseris, Perivolaropoulos 08 Porto, Amendola 08 Linder 07 Constraint t on the growth rate Guzzo et al. 08 redshift space distortion in the clustering of the VIMOS VLT Deep Survey VVDS galaxy This wor : K.Y., Sato, Huetsi measure the monopole spectrum and the quadrupole spectrum of the SDSS LRG sample, detect the redshift-space distortion, measure the growth rate, test the general relativity 3

4 . Redshift-space distortions Kaiser 87, Cole et al. 94, Hamilton 95, etc. Measuring the growth rate through h the redshift-space distortion ti f a d ln D a d ln a 1 = linear velocity field follows δ t m + 1 a V x i i = 0 divv ah a fd 1 Peculiar velocity of galaxy contaminates the observed redshift r r δ z = 1 + z γ V Doppler effect This causes the difference of the spatial clustering between the redshift space and the real space, redshift-space space distortion Oumura, et al., 08 Anisotropic correlation function in SDSS LRGs 4

5 Power spectrum in redshift-space P f b P dfgrs μ is the directional cosine of the angle, P f b P mass μ μ + = dfgrs μ cosθ = μ g between the line of sight direction and the wave number vector. observer r Multipole expansion of P,μ h h l l observer with the Legendre polynomial L l μ = L P P μ μ Taylor Hamilton 96 = = 0,,4,K, l l L l P P μ μ P 0 monopole = + b f b f P P P quadrupole the leading anisotropies b f b f P 5

6 K.Y., Sato, Huetsi, in prep 3. Measurement of monopole and quadrupole of SDSS LRG Luminous Red Galaxy sample in DR5 Redshift distribution of the LRG sample z total survey area 4780 deg. 6

7 K.Y., Sato, Huetsi, in prep. Measurement of the monople P 0 7

8 Measurement of P /P 0 K.Y., Sato, Huetsi Effect of damping function the finger of God Theoretical curve flat ΛCDM model + Ω = 0.8 = 0.96 scale dep. bias m ns h = 0.7 σ = γ 0.56 σ = 360m/s = V 8

9 4. Constraint from the quadrupole spectrum Galaxy power spectrum in redshift-space P, μ = b + f μ Pmass D, μ Monopole and quadrupole 1 Nonlinear velocity effect finger of God Phenomenological damping function D,μ Peacoc, Dodds 94 D, μ = μσ V H 0 Linear redshift-space distortion d ln D1 a f a = d ln a Exponential distribution function for the pair-wise peculiar velocity σ V 9

10 Growth rate as a probe of modified gravity 10

11 Parameterization of the growth rate Linder 05, Lahav 91, Wang, Steinhardt 98, d ln D a Percival 05, 1 γ f a = Ωm a d ln a 1 a Ω m a = H 0 Ωm a H a -3 γ= w z for general relativity include dar energy 0.55 ~ 0.56 = 1 for the DGP model γ 0.68 γ characterizes the difference of the gravity theory, measurement of γ is a simple test of the gravity theory.11

12 3 Clustering bias b δ = bδ galaxy bδ mass If σ 8 is fixed, the clustering bias b is determined d by P 0 P 0 0 b P constraint on γ and σ V 1

13 K.Y., Sato, Huetsi Constraint on γ and σ V Preliminary! γ = 0.44 ± 0.08 σ V = 363±16m/s V 13

14 K.Y., Sato, Huetsi Constraint on γ and σ V Preliminary! γ = 0.51± 0.08 σ V = 366 ±16m/s 14

15 K.Y., Sato, Huetsi Constraint on γ and σ V Preliminary! γ = 0.57 ± 0.08 σ V = 369 ±16m/s 15

16 The constraint on γ γ = σ ± 0.08 σ V = σ ± 4m/s at 1 σ confidence level general relativity γ =0.55~0.56 DGP model γ = This is consistent it t with the general relativity, ltiit however, is inconsistent with the cosmological DGP model, γ=0.68, as long as σ 8 < < cf. σ 8 =0.8±0.036 WMAP 5year 16

17 5. Summary and conclusions We measured the monopole and quadrupole spectra in the spatial clustering of the SDSS LRG galaxy sample. Using the quadrupole spectrum, we measured the γ parameter for the linear growth rate and the pair-wise peculiar velocity dispersion. The measurement of γ is a simple test of the general relativity. The measured value of γ is γ = σ ± at 1 sigma confidence level This is consistent with the general relativity, however, is inconsistent with the cosmological DGP model, γ=0.68, as long as σ 8 is less than

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19 3. Measuring the monopole, quadrupole K.Y., Sato, Huetsi of SDSS LRG Luminous Red Galaxy sample in DR5 19

20 K.Y., Sato, Huetsi 0

21 Measurement of γ and σ V of the SDSS LRG K.Y., Sato, Huetsi WMAP 5year σ 8 =0.8±0.036 σ 8 = 0.75 γ = 0.44 ± 0.08 σ 8 = γ = 0.51± 0.08 σ 8 = 0.85 γ = 0.57 ± 0.08 σ V = 370 ±16m/s 1

22 Clustering bias Ⅰ b hMpc = 1 1/ Clustering bias Ⅱ Determined b to match the observed P 0