We measure the effective distance to z= 0.35, DV(0.35) from the overall shape of the spherically averaged two-point correlation function (2PCF) of the Sloan Digital Sky Survey (SDSS) data release 7 luminous red galaxy sample. We find DV(0.35)=1428+74−73 without assuming a dark energy model or a flat Universe. We find that the derived measurement of (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 .
Combining our results with the cosmic microwave background and supernova data, we obtain and w=−1.010+0.046−0.045 (assuming a constant dark energy equation of state).
We use LasDamas SDSS mock catalogues to compute the covariance matrix of the correlation function and investigate the use of lognormal catalogues as an alternative. We find that the input correlation function can be accurately recovered from lognormal catalogues, although they give larger errors on all scales (especially on small scales) compared to the mock catalogues derived from cosmological N-body simulations.