Redshift space distortions in Lagrangian space and the linear large
  scale velocity field of dark matter
  Untangling the connection between redshift space coordinates, a velocity
measurement, and three dimensional real space coordinates, is a cosmological
problem that is often modeled through a linear understanding of the
velocity-position coupling. This linear information is better preserved in the
Lagrangian space picture of the matter density field. Through Lagrangian space
measurements, we can extract more information and make more accurate estimates
of the linear growth rate of the universe. In this paper, we address the linear
modelling of matter particle velocities through transfer functions, and in
doing so examine to what degree the decrease in correlation with initial
conditions may be contaminated by velocity-based nonlinearities. With a
thorough analysis of the monopole-quadrupole ratio, we find the best-fit value
for the Eulerian velocity dispersion, $\sigma_p = 378.3$ km/s. The covariance
of the cosmological linear growth rate $f$, is estimated in the Eulerian and
Lagrangian cases. Comparing Lagrangian and Eulerian, we find that the error in
$f$ improves by a factor of 3, without the need for nonlinear velocity
dispersion modelling.
