Using Multipoles of the Correlation Function to Measure H(z), D_A(z), and \beta(z) from Sloan Digital Sky Survey Luminous Red Galaxies

TL;DR

This paper introduces a method using effective multipoles of the galaxy two-point correlation function to measure cosmic expansion and geometry parameters from SDSS LRG data, validated with mock catalogs.

Contribution

The paper develops a new approach to extract H(z), D_A(z), and beta(z) from galaxy clustering data using effective multipoles, explicitly accounting for measurement discreteness and validating with mock catalogs.

Findings

Effective multipoles capture most information for parameter constraints.

Using ++ multipoles yields stronger constraints, but + suffices.

Applied to SDSS LRGs, the method provides measurements of H(z), D_A(z), and m^2h^2.

Abstract

Galaxy clustering data can be used to measure the cosmic expansion history H(z), the angular-diameter distance D_A(z), and the linear redshift-space distortion parameter beta(z). Here we present a method for using effective multipoles of the galaxy two-point correlation function (\xi_0(s), \xi_2(s), \xi}_4(s), and \xi_6(s), with s denoting the comoving separation) to measure H(z), D_A(z)$, and beta(z), and validate it using LasDamas mock galaxy catalogs. Our definition of effective multipoles explicitly incorporates the discreteness of measurements, and treats the measured correlation function and its theoretical model on the same footing. We find that for the mock data, \xi_0+\xi_2+\xi_4 captures nearly all the information, and gives significantly stronger constraints on H(z), D_A(z), and beta(z), compared to using only \xi_0+\xi_2. We apply our method to the sample of luminous red galaxies (LRGs) from the Sloan Digital Sky Survey (SDSS) Data Release 7 (DR7) without assuming a dark energy model or a flat Universe. We find that \xi}_4(s) deviates on scales of s<60Mpc/h from the measurement from mock data (in contrast to \xi_0(s), \xi_2(s), and \xi_6(s)), thus we only use \xi_0+\xi_2 for our fiducial constraints. We obtain {H(0.35), D_A(0.35), Omega_mh^2, beta(z)} = {79.6_{-8.7}^{+8.3} km/s/Mpc, 1057_{-87}^{+88}Mpc, 0.103\pm0.015, 0.44\pm0.15} using \xi_0+\xi_2. We find that H(0.35)r_s(z_d)/c and D_A(0.35)/r_s(z_d) (where r_s(z_d) is the sound horizon at the drag epoch) are more tightly constrained: {H(0.35)r_s(z_d)/c, D_A(0.35)/r_s(z_d)} = {0.0437_{-0.0043}^{+0.0041}, 6.48_{-0.43}^{+0.44}\} using \xi_0+\xi_2.