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We study the linear effects of massive neutrinos on the matter densityfluctuations on both large and small scales by solving the fluid equations thatare obtained from Boltzmann hierarchy. These equations set the evolution ofdensity and velocity perturbations of cold dark matter and neutrinos after thelatter become non-relativistic. Due to the free-streaming effects, the massiveneutrinos suppress the total matter power spectrum on small scales whileleaving the large scales untouched. Approximating the neutrino distributionfunction as peaked at one value gives an equation of state that can then beused in an analytic solution of the fluid equations. We then test the validityof fluid approximation with full Boltzmann solvers such as \textsc{class}. Wealso comment on the effects of dark energy on our results.

A Two-Fluid Treatment of the Effect of Neutrinos on the Matter Density