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

Understand

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 $\Omega_mh^2=0.1268 \pm 0.0085$, $H(z=0.35)=81.3\pm 3.8$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 $D_A(0.35)/r_s(z_d)=6.48 \pm 0.25$.