Modelling redshift space distortions in hierarchical cosmologies
  The anisotropy of clustering in redshift space provides a direct measure of
the growth rate of large scale structure in the Universe. Future galaxy
redshift surveys will make high precision measurements of these distortions,
and will potentially allow us to distinguish between different scenarios for
the accelerating expansion of the Universe. Accurate predictions are needed in
order to distinguish between competing cosmological models. We study the
distortions in the redshift space power spectrum in $\Lambda$CDM and
quintessence dark energy models, using large volume N-body simulations, and
test predictions for the form of the redshift space distortions. We find that
the linear perturbation theory prediction by Kaiser (1987) is a poor fit to the
measured distortions, even on surprisingly large scales $k \ge 0.05
h$Mpc$^{-1}$. An improved model for the redshift space power spectrum,
including the non-linear velocity divergence power spectrum, is presented and
agrees with the power spectra measured from the simulations up to $k \sim 0.2
h$Mpc$^{-1}$. We have found a density-velocity relation which is cosmology
independent and which relates the non-linear velocity divergence spectrum to
the non-linear matter power spectrum. We provide a formula which generates the
non-linear velocity divergence $P(k)$ at any redshift, using only the
non-linear matter power spectrum and the linear growth factor at the desired
redshift. This formula is accurate to better than 5% on scales $k<0.2 h
$Mpc$^{-1}$ for all the cosmological models discussed in this paper. Our
results will extend the statistical power of future galaxy surveys.
