  We discuss the propagation of dark matter perturbations with non-zero
velocity dispersion in cosmological models. In particular a non-zero massive
neutrino component may well have a significant effect on the matter power
spectrum and cosmic microwave background anisotropy. We present a covariant
analysis of the evolution of a dark matter distribution via a two-dimensional
momentum-integrated hierarchy of multipole equations. This can be expanded in
the velocity weight to provide accurate approximate equations if the matter is
non-relativistic, and we also perform an expansion in the mass to study the
propagation of relativistic matter perturbations. We suggest an approximation
to the exact hierarchy that can be used to calculate efficiently the effect of
the massive neutrinos on the CMB power spectra. We implement the corresponding
scalar mode equations numerically achieving a considerable reduction in
computation time compared with previous approaches.
