Towards a non-Gaussian model of redshift space distortions
  To understand the nature of the accelerated expansion of the Universe, we
need to combine constraints on the expansion rate and growth of structure. The
growth rate is usually extracted from three dimensional galaxy maps by
exploiting the effects of peculiar motions on galaxy clustering. However,
theoretical models of the probability distribution function (PDF) of galaxy
pairwise peculiar velocities are not accurate enough on small scales to reduce
the error on theoretical predictions to the level required to match the
precision expected for measurements from future surveys. Here, we improve the
modelling of the pairwise velocity distribution by using the Skew-T PDF, which
has nonzero skewness and kurtosis. Our model accurately reproduces the
redshift-space multipoles (monopole, quadrupole and hexadecapole) predicted by
N-body simulations, above scales of about $10\,h^{-1}{\rm Mpc}$. We illustrate
how a Taylor expansion of the streaming model can reveal the contributions of
the different moments to the clustering multipoles, which are independent of
the shape of the velocity PDF. The Taylor expansion explains why the Gaussian
streaming model works well in predicting the first two redshift-space
multipoles, although the velocity PDF is non-Gaussian even on large scales.
Indeed, any PDF with the correct first two moments would produce precise
results for the monopole down to scales of about $10\,h^{-1}{\rm Mpc}$, and for
the quadrupole down to about $30\,h^{-1}{\rm Mpc}$. An accurate model for the
hexadecapole needs to include higher-order moments.
