The collisionless damping of density fluctuations in an expanding universe

Temporal evolution calculations are undertaken for the early universe's initially adiabatic density fluctuation spectrum, by means of the numerical integration of the coupled Einstein-Boltzmann equations for scalar perturbations in the metric and in the density of photons, neutrinos, and collisionless relics. The linear perturbation spectrum is shown to be characterized by two scales, namely the damping mass and the horizon mass, when the energy density in relativistic particles equals that in nonrelativistic ones. For massive neutrinos, both scales are of supercluster size, and the Zel'dovich 'pancake' hypothesis, in which a large scale is the first to collapse, is expected irrespective of initial spectrum. For massive gravitations, the damping mass is of galactic scale.