Cosmological Vlasov–Poisson equations for dark matter

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