Phase-space perturbation theory for cosmic large-scale structure

TL;DR

This paper introduces a perturbative method for cosmic structure formation that avoids truncating the momentum hierarchy, enabling analysis of velocity dispersion effects and serving as a basis for advanced techniques.

Contribution

It develops a non-truncating perturbative framework for the Vlasov-Poisson system, capturing velocity dispersion and higher cumulants dynamically.

Findings

Recovers standard perturbation theory for cold initial conditions.

Shows higher momentum cumulants are generated by velocity dispersion.

Provides analytical large-scale approximations supporting numerical solutions.

Abstract

We consider a perturbative approach to the Vlasov-Poisson system for cosmic structure formation that does not rely on any truncation of the momentum-cumulant hierarchy. The generally non-trivial linear solution is computed by solving a Volterra-type integral equation and higher orders are obtained recursively. As expected, the results of Eulerian standard perturbation theory are recovered for perfectly cold initial conditions. Deviating slightly from the latter by introducing a homogeneous and isotropic initial velocity dispersion, we show that all higher momentum cumulants are generated dynamically at any perturbative order. We support our numerical solutions by an analytical large-scale approximation. Our approach serves as a basis for exploring different background-perturbation splits of the phase-space density and non-perturbative techniques.