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

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 (ξ_0(s), ξ_2(s), ξ}_4(s), and ξ_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, ξ_0+ξ_2+ξ_4 captures nearly all the information, and gives significantly stronger constraints on H(z), D_A(z), and beta(z), compared to using only ξ_0+ξ_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 ξ}_4(s) deviates on scales of s<60Mpc/h from the measurement from mock data (in contrast to ξ_0(s), ξ_2(s), and ξ_6(s)), thus we only use ξ_0+ξ_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 ξ_0+ξ_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 ξ_0+ξ_2.