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Interpreting large-scale redshift-space distortion measurements

The simplest theory describing large-scale redshift-space distortions (RSD), based on linear theory and distant galaxies, depends on the growth of cosmological structure, suggesting that strong tests of General Relativity can be constructed from galaxy surveys. As data sets become larger and the expected constraints more precise, the extent to which the RSD follow the simple theory needs to be assessed in order that we do not introduce systematic errors into the tests by introducing inaccurate simplifying assumptions. We study the impact of the sample geometry, non-linear processes, and biases induced by our lack of understanding of the radial galaxy distribution on RSD measurements. Using LasDamas simulations of the Sloan Digital Sky Survey II (SDSS-II) Luminous Red Galaxy (LRG) data, these effects are shown to be important at the level of 20 per cent. Including them, we can accurately model the recovered clustering in these mock catalogues on scales 30 -- 200 Mpc/h. Applying this analysis to robustly measure parameters describing the growth history of the Universe from the SDSS-II data, gives $f(z=0.25)σ_8(z=0.25)=0.3512\pm0.0583$ and $f(z=0.37)σ_8(z=0.37)=0.4602\pm0.0378$ when no prior is imposed on the growth-rate, and the background geometry is assumed to follow a $Λ$CDM model with the WMAP + SNIa priors. The standard WMAP constrained $Λ$CDM model with General Relativity predicts $f(z=0.25)σ_8(z=0.25)=0.4260\pm0.0141$ and $f(z=0.37)σ_8(z=0.37)=0.4367\pm0.0136$, which is fully consistent with these measurements.