Extending recovery of the primordial matter power spectrum

Abstract

The shape of the primordial matter power spectrum encodes critical information on cosmological parameters. At large scales, in the linear regime, the observable galaxy power spectrum P obs(k) is expected to follow the shape of the linear matter power spectrum P lin(k), but on smaller scales the effects of nonlinearity and galaxy bias make the ratio P obs(k)/P lin(k) scale dependent. We develop a method that can extend the dynamic range of the primordial matter power spectrum recovery, taking full advantage of precision measurements on quasi-linear scales, by incorporating additional constraints on the galaxy halo occupation distribution (HOD) from the projected galaxy correlation function wp (r p ). We devise an analytic model to calculate observable galaxy power spectrum P obs(k) in real space and redshift space, given P lin(k) and HOD parameters, and we demonstrate its accuracy at the few percent level with tests against a suite of populated N-body simulations. Once HOD parameters are determined by fitting wp (rp ) measurements for a given cosmological model, galaxy bias is completely specified, and our analytic model predicts both the shape and normalization of P obs(k). Applying our method to the main galaxy redshift samples from the Sloan Digital Sky Survey (SDSS), we find that the real-space galaxy power spectrum follows the shape of the nonlinear matter power spectrum at the 1%-2% level up to k = 0.2 h Mpc-1 and that current observational uncertainties in HOD parameters leave only few percent uncertainties in our scale-dependent bias predictions up to k = 0.5 h Mpc-1. These uncertainties can be marginalized over in deriving cosmological parameter constraints, and they can be reduced by higher precision wp (r p ) measurements. When we apply our method to the SDSS luminous red galaxy (LRG) samples, we find that the linear bias approximation is accurate to 5% at k ≤ 0.08 h Mpc-1, but the strong scale dependence of LRG bias prevents the use of linear theory at k ≥ 0.08 h Mpc-1. Our HOD model prediction is in good agreement with the recent SDSS LRG power spectrum measurements at all measured scales (k ≤ 0.2 h Mpc-1), naturally explaining the observed shape of P obs(k) in the quasi-linear regime. The phenomenological "Q-model" prescription is a poor description of galaxy bias for the LRG samples, and it can lead to biased cosmological parameter estimates when measurements at k ≥ 0.1 h Mpc -1 are included in the analysis. We quantify the potential bias and constraints on cosmological parameters that arise from applying linear theory and Q-model fitting, and we demonstrate the utility of HOD modeling of high-precision measurements of P obs(k) on quasi-linear scales, which will be obtainable from the final SDSS data set. © 2009. The American Astronomical Society.