Measurement of $H(z)$ and $D_A(z)$ from the two-dimensional power spectrum of Sloan Digital Sky Survey luminous red galaxies

Abstract

We present a method to measure the Hubble parameter $H(z)$ and the angular diameter distance $D_A(z)$ simultaneously from the two-dimensional matter power spectrum from galaxy surveys with broad sky coverage. We validate this method by applying it to the LasDamas mock galaxy catalogs. Then we apply this method to Sloan Digital Sky Survey (SDSS) Data Release 7 and obtain measurements of $Ω_mh^2=0.1268 \pm 0.0085$, $H(z=0.35)=81.3\pm 3.8$km/s/Mpc, $D_A(z=0.35) = 1037\pm44$Mpc, without assuming a dark energy model or a flat universe. We also find that the derived parameters $H(0.35)r_s(z_d)/c=0.0431 \pm 0.0018$ and $D_A(0.35)/r_s(z_d)=6.48 \pm 0.25$. These are in excellent agreement with similar measurements from the two-dimensional correlation function of the same data.