Linear dark matter density perturbations: A Wigner approach

Abstract

In the Newtonian regime, the dynamics of scalar field dark matter is governed by the Schrödinger-Poisson model. In the usual treatment, the model is represented in a hydrodynamic form, by introducing macroscopic quantities such as the density and the average velocity. Here, we discuss an alternative kinetic representation of the same model, by relying on the Wigner function. This representation contains the hydrodynamic formulation as a special case but allows accounting for possible velocity dispersion while the hydrodynamic representation allows none. It has also the advantage of making more explicit the limit, yielding the Vlasov regime. We discuss in particular the effect of the broadening of the Wigner function, arising from the statistical properties of the wave function, and show that it gives rise to a Landau-like damping that tends to suppress the gravitational instability for larger wave-length perturbations.