Probing the matter power spectrum with the clustering ratio of - PowerPoint PPT Presentation

Frontiers of Fundamental Physics (Marseille, July 2014) Probing the matter power spectrum with the clustering ratio of galaxies Bel & Marinoni 2014, A&A, 563, 36 Bel, Marinoni, Granett, Guzzo, Peacock et al. (The VIPERS Team) 2014, , A&A, 563, 37 Bel, Brax, Marinoni & Valageas 2014, submitted, arXiv: 1406.3347B Julien BEL Osservatorio Astronomico di Brera ( with L. Guzzo) Collaborators: P. BRAX, C. MARINONI and P. VALAGEAS

Outline • Goal: fixing the matter power spectrum • Tool: a new clustering statistic, the clustering ratio • Test: simulations • Results: -Omega_m from SDSS DR7 and VIPERS PDR1 -f R 0 from SDSS DR7 and DR10 2

The Matter power spectrum Perturbation Theory 3

The Matter power spectrum Perturbation Theory b δ N i i ∑ δ = g , R R i ! i 0 = Fry & Gazta ñ aga (1993) 3

The Matter power spectrum Perturbation Theory b δ N i i ∑ δ = g , R R i ! i 0 = Fry & Gazta ñ aga (1993) 2 f 2 δ R z = δ g , R + µ k δ g , R Kaiser (1987) 3

Statistical properties of smoothed over-densities Variance of fluctuations in spheres: 2 (  2 x ) σ g , R = δ g , R R 4

Statistical properties of smoothed over-densities Variance of fluctuations in spheres: 2 (  2 x ) σ g , R = δ g , R 2-point correlation function: ξ g , R ( r ) = δ g , R (  ) δ g , R (  x +  x r ) r R 4

Statistical properties of smoothed over-densities Perturbation Theory DEC DEC RA Survey description in Guzzo et al. (arXiv:1303.2623G) and data 5 access to PDR-1 in Garilli et al. (arXiv:1310.1008G)

Statistical properties of smoothed over-densities Perturbation Theory DEC DEC RA Survey description in Guzzo et al. (arXiv:1303.2623G) and data 5 access to PDR-1 in Garilli et al. (arXiv:1310.1008G)

Statistical properties of smoothed over-densities Perturbation Theory DEC DEC RA Survey description in Guzzo et al. (arXiv:1303.2623G) and data 5 access to PDR-1 in Garilli et al. (arXiv:1310.1008G)

Dynamics of the inhomogeneous universe Perturbation Theory   ( t , x ) ( t ) ρ − ρ ( t , x ) ρ δ = ρ ρ ( t ) ρ    x x x Homogeneous Background Deviations on smaller scales d 2 δ dt 2 + 2 H d δ dt − 3 2 Ω m H 2 δ = 0 Linear evolution of fluctuations: (In Newtonian approximation) 6

Dynamics of the inhomogeneous universe Perturbation Theory   ( t , x ) ( t ) ρ − ρ ( t , x ) ρ δ = ρ ρ ( t ) ρ    x x x Homogeneous Background Deviations on smaller scales d 2 δ dt 2 + 2 H d δ dt − 3 2 Ω m H 2 δ = 0 Linear evolution of fluctuations: (In Newtonian approximation) # & − g R + f ( R ) d 4 x ∫ S = + L m Modification of Einstein-Hilbert action: % ( $ 16 π G ' (Starobinsky 1980) f ( R ) = − 2 Λ − c 2 f R 0 N + 1 R 0 Power law function of the Ricci scalar : R N N (Carroll et al. 2007, Sotiriou 2010) 7

Dynamics of the inhomogeneous universe Perturbation Theory   ( t , x ) ( t ) ρ − ρ ( t , x ) ρ δ = ρ ρ ( t ) ρ    x x x Homogeneous Background Deviations on smaller scales d 2 δ dt 2 + 2 H d δ dt − 3 2 Ω m H 2 δ g eff ( k ) = 0 Linear evolution of fluctuations: (In Newtonian approximation) k 2 / 3 g eff ( k ) = 1 + Scale dependency : a 2 m 2 + k 2 m − 2 ≡ 3 d 3 f Ricci scalar: N + 1 d 3 R = − 3( N + 1) f R 0 c 2 R 0 ! $ R ( a ) = 6 2 H 2 + dH R N + 2 # & " dt % 7

Statistical properties of smoothed over-densities 2 ( z ) = D 2 ( z ). σ 8 2 (0). F σ R variance of smoothed matter field: R 2-point correlation function of smoothed matter field: ξ R ( r , z ) = D 2 ( z ). σ 8 2 (0). G R ( r ) 8

Statistical properties of smoothed over-densities 2 ( z ) = σ 8 2 (0). F R ( z ) σ R variance of smoothed matter field: 2 (0). G R ( r , z ) ξ R ( r , z ) = σ 8 2-point correlation function of smoothed matter field: 8

Statistical properties of smoothed over-densities 2 ( z ) = σ 8 2 (0). F R ( z ) σ R variance of smoothed matter field: 2 (0). G R ( r , z ) ξ R ( r , z ) = σ 8 2-point correlation function of smoothed matter field: + ∞ + ∞ 2 2 ( ) ( ) ( ) W kR d ln k ( z ) W kR j kr d ln k ∫ Δ ∫ Δ k TH k TH 0 0 0 F G ( r ) and = = R R + ∞ + ∞ 2 2 ( ) ( ) W kr d ln k ( z ) W kr d ln k ∫ Δ ∫ Δ k TH 8 k TH 8 0 0 3 4 k P ( k ) is the dimensionless power spectrum Δ = π where k 3 [ ] W TH ( kR ) sin( kR ) kR cos( kR ) and = − 3 ( kR ) Bel & Marinoni 2012 (MNRAS) 8

Statistical properties of smoothed over-densities 2 ( z ) = σ 8 2 (0). F R ( z ) σ R variance of smoothed matter field: 2 (0). G R ( r , z ) ξ R ( r , z ) = σ 8 2-point correlation function of smoothed matter field: + ∞ + ∞ 2 2 ( ) ( ) ( ) W kR d ln k ( z ) W kR j kr d ln k ∫ Δ ∫ Δ k TH k TH 0 0 0 F G ( r ) and = = R R + ∞ + ∞ 2 2 ( ) ( ) W kr d ln k ( z ) W kr d ln k ∫ Δ ∫ Δ k TH 8 k TH 8 0 0 • Redshift evolution • Non linear bias • Redshift distortions 8

The clustering ratio The galaxy clustering ratio: The matter clustering ratio: η g , R ( r ) ≡ ξ g , R ( r ) η R ( r ) = G R ( r ) 2 F R σ g , R 1 δ + b 2 δ 2 + ... Bias between galaxy and matter fluctuations: δ g = b 0 + b 2 If the second order bias coefficient satisfies to | b 2 / b 1 | < 1 z ( r ) = η R ( r ) η g , R 9

The clustering ratio The galaxy clustering ratio: The matter clustering ratio: η g , R ( r ) ≡ ξ g , R ( r ) η R ( r ) = G R ( r ) 2 F R σ g , R 1 δ + b 2 δ 2 + ... Bias between galaxy and matter fluctuations: δ g = b 0 + b 2 If the second order bias coefficient satisfies to | b 2 / b 1 | < 1 z ( r ) = η R ( r ) η g , R What you see (clustering of galaxies) is what you get (clustering of matter) 9

The clustering ratio Vs Galaxy bias Impact of scale dependent bias: Analysis performed on HOD galaxy mock catalogues described in de la Torre et al. (2013) 10

The clustering ratio as a cosmological test The galaxy clustering ratio: The matter clustering ratio: η g , R ( r ) ≡ ξ g , R ( r ) η R ( r ) = G R ( r ) 2 F R σ g , R z ( r ) = η R ( r ) η g , R Alcock-Paczynski Power spectrum 11

The clustering ratio as a cosmological test z ~1     z ( r , z ( r , )/ η g , R true ) − 1 η g , R Ω Ω η R ( r , )/ η R ( r , true ) − 1 Ω Ω 12

SDSS DR7 + VIPERS PDR1 Planck 13

Measuring the f R 0 parameter of modified gravity The galaxy clustering ratio: The matter clustering ratio: η g , R ( r ) ≡ ξ g , R ( r ) η R ( r , z ) = G R ( r , z ) 2 F R ( z ) σ g , R z ( r ) = η R ( r ) η g , R Fixed by the expansion rate Power spectrum (Planck) d 2 δ dt 2 + 2 H d δ dt − 3 2 Ω m H 2 δ g eff ( k ) = 0 14

Sloan Digital Sky Survey Data Release 7 + 10 The galaxy clustering ratio: The matter clustering ratio: η g , R ( r ) ≡ ξ g , R ( r ) η R ( r ) = G R ( r ) 2 F R σ g , R η g , R ( r ) = η R ( r ) Alcock-Paczynski Power spectrum 15

Constraints of deviation from Einstein’s gravity th ( z i )) 2 3 ( η g , R ( z i ) − η R χ 2 = ∑ Likelihood analysis: 2 σ i i = 1 η g , R ( r ) = η R ( r ) Alcock-Paczynski Power spectrum f ( R ) = − 2 Λ − c 2 f R 0 N + 1 R 0 16 R N N

Conclusions • A new clustering statistic: the galaxy clustering ratio η g , R = ξ g , R σ 2 g , R - Its amplitude is the same for galaxies and matter - It is weakly affected by redshift-space distortions - The estimator is simple (count-in-cell) and robust (tests on simulations) • Assuming a flat LambdaCDM universe and combining VIPERS and SDSS measurements Ω m = 0.274 ± 0.017 • Adapted to cosmological tests of gravitation (quasi-linear scale) • Assuming Planck LCDM background cosmology f R 0 < 3 × 10 − 6 • Next: include massive neutrinos and constrain their mass 17

The clustering ratio in the weakly non linear regime The galaxy clustering ratio: η g , R ( r ) ≡ ξ g , R ( r ) 1 h -3 Gpc 3 comoving 2 σ g , R output at z=1 of MultiDark simulation Smith et al. (2003 ) (Prada et al. 2012) Linear 14 millions of Haloes with masses n = r between 10 11.5 h -1 R and 10 14.5 h -1 solar masses 10

The clustering ratio Vs Halo bias Real space (comoving output): Redshift space (light cone): η g , R ( r ) ≡ ξ g , R ( r ) η R ( r ) = G R ( r ) 2 F R σ g , R What you see (clustering of galaxies) is what you get (clustering of matter) n = r R = 3 11

Luminosity dependence in SDSS 11

Application of the strategy (SDSS) η R L inear P erturbation T heory (weak) (strong) PRIORS: PRIORS: 0 1 ≤ Ω ≤ m • On Ho from HST 0 1 ≤ Ω ≤ • On baryonic X 1 . 5 w 0 . 5 density from Ω − ≤ ≤ − Likelihood X BigBang 0 . 4 h 1 ≤ ≤ Nucleosynthesis 2 0 . h 0 . 03 ≤ Ω ≤ • On the spectral b index from CMB 0 . 9 n 1 . 1 ≤ ≤ s D istance - ESTIMATOR R edshift R elation η g , R 11