Landau damping on expanding backgrounds

TL;DR

This paper demonstrates nonlinear Landau damping in an expanding Newtonian cosmological plasma model, showing superpolynomial decay of charge density contrast for certain expansion rates and initial data conditions.

Contribution

It is the first to establish Landau damping in a cosmological setting, analyzing the Vlasov-Poisson system on an expanding torus with specific decay results.

Findings

Solutions exhibit superpolynomial decay of charge density contrast.

Decay rates depend on the expansion rate parameter q.

Initial data in a strong Gevrey class is required for damping.

Abstract

We analyse the effect of expansion in Newtonian cosmology on the asymptotic behaviour of charged self-interacting plasmas close to Poisson equilibria. To this end, we study the Vlasov-Poisson system on the phase space of a $3$-torus which is expanding with respect to the scale factor $a(t)$. We show that, for $a(t)=t^q$ with $q\in(0,\frac12)$, solutions to this system exhibit nonlinear Landau damping for initial data that is small with respect to a suitably strong Gevrey class, i.e., the charge density contrast of the plasma decays superpolynomially. For larger choices of $q$ within this range, the initial data requirements become stricter while the decay weakens. To our knowledge, this is the first result showing Landau damping in a cosmological setting.