Vlasov Perturbation Theory applied to $\Lambda$CDM

TL;DR

This paper extends perturbation theory for cosmological matter distribution by incorporating velocity dispersion effects, leading to more accurate, cutoff-independent predictions of the matter power spectrum in $\Lambda$CDM models, validated against simulations.

Contribution

It introduces Vlasov Perturbation Theory (VPT) with velocity dispersion, providing a stable, efficient alternative to standard methods for modeling non-linear cosmic structures.

Findings

VPT agrees with simulations up to missing three-loop effects.

Treating dispersion as a free parameter yields stable predictions.

Two-loop power spectrum is robust to neglecting higher cumulants.

Abstract

We apply the framework of Vlasov Perturbation Theory (VPT) to the two-loop matter power spectrum within $\Lambda$CDM cosmologies. The main difference to Standard Perturbation Theory (SPT) arises from taking the velocity dispersion tensor into account, and the resulting screening of the backreaction of UV modes renders loop integrals cutoff-independent. VPT is informed about non-perturbative small scale dynamics via the average value of the dispersion generated by shell-crossing, which impacts the evolution of perturbations on weakly non-linear scales. When using an average dispersion from halo models, the VPT power spectrum agrees with the one from the simulation, up to differences from missing three-loop contributions. Alternatively, treating the average dispersion as free parameter we find a remarkably stable prediction of the matter power spectrum from collisionless dynamics at percent level for a wide range of the dispersion scale. We quantify the impact of truncating the Vlasov hierarchy for the cumulants of the phase-space distribution function, finding that the two-loop matter power spectrum is robust to neglecting third and higher cumulants. Finally, we introduce and validate a simplified fast scheme fVPT that can be easily incorporated into existing codes and is as numerically efficient as SPT.