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 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.
