We investigate the use of the cross-correlation between galaxies and galaxy groups to measure redshift-space distortions (RSD) and thus probe the growth rate of cosmological structure. This is compared to the classical approach based on using galaxy
auto-correlation. We make use of realistic simulated galaxy catalogues that have been constructed by populating simulated dark matter haloes with galaxies through halo occupation prescriptions. We adapt the classical RSD dispersion model to the case of the group-galaxy cross-correlation function and estimate the RSD parameter $beta$ by fitting both the full anisotropic correlation function $xi(r_p,pi)$ and its multipole moments. In addition, we define a modified version of the latter statistics by truncating the multipole moments to exclude strongly non-linear distortions at small transverse scales. We fit these three observable quantities in our set of simulated galaxy catalogues and estimate statistical and systematic errors on $beta$ for the case of galaxy-galaxy, group-group, and group-galaxy correlation functions. When ignoring off-diagonal elements of the covariance matrix in the fitting, the truncated multipole moments of the group-galaxy cross-correlation function provide the most accurate estimate, with systematic errors below 3% when fitting transverse scales larger than $10Mpc/h$. Including the full data covariance enlarges statistical errors but keep unchanged the level of systematic error. Although statistical errors are generally larger for groups, the use of group-galaxy cross-correlation can potentially allow the reduction of systematics while using simple linear or dispersion models.
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 on redshift measurement errors, on the
reconstruction of the underlying real-space clustering and 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 and apply the standard linear dispersion model to fit the anisotropy of the observed correlation function. We verify that redshift errors up to ~0.2% have a negligible impact on the precision with which the specific growth rate beta 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% due to the limitations of the linear dispersion model, which is studied in a separate paper. We then show that 50% of the statistical error budget on beta depends on the deprojection procedure through which the real-space correlation function 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 beta and OmegaM. In a volume of 2.4(Gpc/h)^3, the correct OmegaM is obtained with ~12% error and negligible bias, once the real-space correlation function is properly reconstructed.
