Cosmology with clustering anisotropies : disentangling dynamic and geometric distortions in galaxy redshift surveys

We investigate the impact of different observational effects affecting a precise and accurate measurement of the growth rate of fluctuations from the anisotropy of clustering in galaxy redshift surveys. We focus here on redshift measurement errors, on the reconstruction of the underlying real-space clustering and, most importantly, on the apparent degeneracy existing with the geometrical distortions induced by the cosmology-dependent conversion of redshifts into distances. We use a suite of mock catalogues extracted from large N-body simulations, focusing on the analysis of intermediate, mildly non-linear scales (r < 50 h−1 Mpc) and apply the standard ‘dispersion model’ to fit the anisotropy of the observed correlation function ξ(r⊥, r∥) . We first verify that redshift errors up to δz ∼ 0.2 per cent (i.e. σz ∼ 0.002 at z = 1) have a negligible impact on the precision with which the specific growth rate β can be measured. Larger redshift errors introduce a positive systematic error, which can be alleviated by adopting a Gaussian distribution function of pairwise velocities. This is, in any case, smaller than the systematic error of up to 10 per cent due to the limitations of the dispersion model, which is studied in a separate paper. We then show that 50 per cent of the statistical error budget on β depends on the deprojection procedure through which the real-space correlation function, needed for the modelling process, is obtained. Finally, we demonstrate that the degeneracy with geometric distortions can in fact be circumvented. This is obtained through a modified version of the Alcock–Paczynski test in redshift space, which successfully recovers the correct cosmology by searching for the solution that optimizes the description of dynamical redshift distortions. For a flat cosmology, we obtain largely independent, robust constraints on β and on the mass density parameter, ΩM. In a volume of 2.4 (h−1 Gpc)3, the correct ΩM is obtained with ∼12 per cent error and negligible bias, once the real-space correlation function is properly reconstructed.