A Two-Fluid Treatment of the Effect of Neutrinos on the Matter Density
  We study the linear effects of massive neutrinos on the matter density
fluctuations on both large and small scales by solving the fluid equations that
are obtained from Boltzmann hierarchy. These equations set the evolution of
density and velocity perturbations of cold dark matter and neutrinos after the
latter become non-relativistic. Due to the free-streaming effects, the massive
neutrinos suppress the total matter power spectrum on small scales while
leaving the large scales untouched. Approximating the neutrino distribution
function as peaked at one value gives an equation of state that can then be
used in an analytic solution of the fluid equations. We then test the validity
of fluid approximation with full Boltzmann solvers such as \textsc{class}. We
also comment on the effects of dark energy on our results.
