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

TL;DR

This paper reviews recent theoretical advances in analyzing the Vlasov-Poisson equations governing dark matter evolution, highlighting connections to plasma physics and providing insights into the formation of cosmic structures.

Contribution

It presents new elementary methods for analyzing infinite densities in dark matter distributions and explores links between cosmological and plasma physics problems.

Findings

Mathematical analysis of infinite densities in dark matter

Connections established between cosmological and plasma physics problems

Recent progress enables elementary analysis of complex dark matter structures

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.