A Robust Distance Measurement and Dark Energy Constraints from the Spherically-Averaged Correlation Function of Sloan Digital Sky Survey Luminous Red Galaxies

TL;DR

This paper measures the effective distance to redshift 0.35 using SDSS LRG data, constraining dark energy parameters and the Hubble constant with minimal model assumptions, and assesses systematic uncertainties with mock catalogs.

Contribution

It provides a robust, model-independent measurement of the distance scale from the SDSS LRG correlation function and evaluates the use of lognormal catalogs for covariance estimation.

Findings

Measured D_V(0.35)=1428_{-73}^{+74} Mpc.

Derived tight constraint on r_s(z_d)/D_V(0.35)=0.1143 ± 0.0030.

Estimated H(0.35)=83^{+13}_{-15} km/s/Mpc and D_A(0.35)=1089^{+93}_{-87} Mpc.

Abstract

We measure the effective distance to z=0.35, D_V(0.35), from the overall shape of the spherically-averaged two-point correlation function of the Sloan Digital Sky Survey (SDSS) Data Release 7 (DR7) luminous red galaxy (LRG) sample. We find D_V(0.35)=1428_{-73}^{+74} without assuming a dark energy model or a flat Universe. We find that the derived measurement of r_s(z_d)/D_V(0.35)=0.1143 \pm 0.0030 (the ratio of the sound horizon at the drag epoch to the effective distance to z=0.35) is more tightly constrained and more robust with respect to possible systematic effects. It is also nearly uncorrelated with \Omega_m h^2. Combining our results with the cosmic microwave background and supernova data, we obtain \Omega_k=-0.0032^{+0.0074}_{-0.0072} and w=-1.010^{+0.046}_{-0.045} (assuming a constant dark energy equation of state). By scaling the spherically-averaged correlation function, we find the Hubble parameter H(0.35)=83^{+13}_{-15} km s^{-1}Mpc^{-1} and the angular diameter distance D_A(0.35)=1089^{+93}_{-87} Mpc. We use LasDamas SDSS mock catalogs to compute the covariance matrix of the correlation function, and investigate the use of lognormal catalogs as an alternative. We find that the input correlation function can be accurately recovered from lognormal catalogs, although they give larger errors on all scales (especially on small scales) compared to the mock catalogs derived from cosmological N-body simulations.