The collisionless damping of density fluctuations in an expanding universe

Abstract

The best candidate for the dark matter is a massive collisionless non-baryonic relic of the early universe. The most natural type of initial density fluctuations expected are of the adiabatic rather than of the isothermal type. We calculate the temporal evolution of the (initially adiabatic) fluctuation spectrum by numerical integration of the coupled Einstein-Boltzmann equations for scalar perturbations in the metric and in the density of photons, neutrinos, and collisionless relics. Our output linear perturbation spectrum, which is itself input to the nonlinear problem of large scale structure formation, is shown to be characterized by two scales: the damping mass and the horizon mass when the energy density in relativistic particles equals that in nonrelativistic ones, M/sub H/eq. Collisionless relics which decouple when relativistic may be of two basic types if they are to dominate the mass of the universe: massive neutrinos of 10--100 eV, or massive gravitinos (or other weakly interacting particles) of mass about 1 keV. For massive neutrinos, both scales are of supercluster size; and the Zel'dovich pancake picture, in which a large scale is the first to collapse, is expected, regardless of initial spectrum. For massive gravitinos, the damping mass is of galactic scale. Depending uponmore » the initial spectrum, one can get either hierarchical clustering from the damping scale upward or fragmentation of the large M/sub H/eq scale. Collisionless relics which decouple when nonrelativistic have negligible damping masses; again, hierarchical clustering from very small scales or large scale fragmentation is possible in this adiabatic picture.« less