Large-scale peculiar velocity fields: Newtonian vs relativistic
  treatment
  We employ a perturbative analysis to study the evolution of large-scale
peculiar velocity fields within the framework of Newtonian gravity and then
compare our results to those of the corresponding relativistic treatment. In so
doing, we use the same mathematical formalism and apply the same physical
approach. This facilitates a direct and transparent comparison between the two
treatments. Our study recovers and extends the familiar Newtonian results on
the one hand, while on the other it shows that the Newtonian analysis leads to
substantially weaker growth-rates for the peculiar velocity field, compared to
the relativistic approach. This implies that, by using Newton's rather than
Einstein's theory, one could seriously underestimate the overall kinematic
evolution of cosmological peculiar motions. We are also in the position to
identify the reason the two theories arrive at such considerably different
results and conclusions.
