Measuring Cosmological Parameters using Matter Power Spectrum from Galaxy Redshift Survey Data

The galaxy power spectrum is a powerful tool used to study cosmic large scale structure and dark energy. A method to obtain the one dimensional galaxy power spectrum using the direct Fourier method is presented and this technique was applied to two degree field Galaxy Redshift Survey (2dFGRS) data and Sloan Digital Sky Survey (SDSS) data separately. Although this method is slow compared to fast Fourier transform, it is more accurate at small scales. The two dimensional matter power spectrum was only obtained using surveys with narrow sky coverage until now. The method presented here is applicable to any current or future survey with wider sky coverage. A method to measure the Hubble parameter H(z) and the angular diameter distance DA (z) simultaneously from the two-dimensional matter power spectrum is also presented. The method is validated by applying it to the LasDamas mock galaxy catalogs. Then, this method is applied to Sloan Digital Sky Survey (SDSS) Data Release 7 to measure two dimensional galaxy power spectrum and obtain measurements of Ωm h2 = 0.1268 ± 0.0085, H(z = 0.35) = 81.3 ± 3.8km/s/Mpc, DA (z = 0.35) = 1037 ± 44Mpc, without assuming a dark energy model or a flat universe. The derived parameters H(0.35)rs (zd )/c = 0.0431 ± 0.0018 and DA (0.35)/rs (zd ) = 6.48 ± 0.25 are also measured and these are in excellent agreement with similar measurements from the two-dimensional correlation function of the same data.