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

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 Ω_m h^2. Combining our results with the cosmic microwave background and supernova data, we obtain Ω_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.