Cosmological Vlasov-Poisson equations for dark matter: Recent developments and connections to selected plasma problems

Abstract

The cosmic large-scale structures of the Universe are mainly the result of the gravitational instability of initially small density fluctuations in the dark-matter distribution. Dark matter appears to be initially cold and behaves as a continuous and collisionless medium on cosmological scales, with evolution governed by the gravitational Vlasov-Poisson equations. Cold dark matter can accumulate very efficiently at focused locations, leading to a highly non-linear filamentary network with extreme matter densities. Traditionally, investigating the non-linear Vlasov-Poisson equations was typically reserved for massively parallelised numerical simulations. Recently, theoretical progress has allowed us to analyse the mathematical structure of the first infinite densities in the dark-matter distribution by elementary means. We review related advances, as well as provide intriguing connections to classical plasma problems, such as the beam-plasma instability.

Making (dark matter) waves: Untangling wave interference for multi-streaming dark matter

“…Equations of Schrödinger-Poisson type can also be derived as an alternate scheme for closing the Vlasov cumulant hierarchy which appears in CDM dynamics (see e.g. Rampf (2021) for a recent review of the cosmological Vlasov-Poisson equations). If one requires that the cumulant generating function is constructed only from the density and velocity (the first two cumulants) degrees of freedom, then the resulting cumulant generating function takes the form of Schrödinger-Poisson (Uhlemann 2018).…”