Perturbation theory with dispersion and higher cumulants: non-linear regime

TL;DR

This paper develops a non-linear perturbation theory for dark matter clustering that incorporates dispersion and higher cumulants, improving predictions of power spectra and bispectra, especially in regimes where standard perturbation theory diverges.

Contribution

It introduces a Vlasov Perturbation Theory framework that includes dispersion effects, demonstrating its effectiveness in modeling non-linear gravitational clustering and extending perturbative calculations beyond traditional limits.

Findings

VPT kernels exhibit UV mode screening, enabling non-linear corrections for blue spectra.

Good agreement with N-body simulations up to the non-linear scale across various spectral indices.

Vorticity and vector modes are essential for momentum conservation and accurate large-scale behavior.

Abstract

We present non-linear solutions of Vlasov Perturbation Theory (VPT), describing gravitational clustering of collisionless dark matter with dispersion and higher cumulants induced by orbit crossing. We show that VPT can be cast into a form that is formally analogous to standard perturbation theory (SPT), but including additional perturbation variables, non-linear interactions, and a more complex propagation. VPT non-linear kernels have a crucial decoupling property: for fixed total momentum, the kernels becomes strongly suppressed when any of the individual momenta cross the dispersion scale into the non-linear regime. This screening of UV modes allows us to compute non-linear corrections to power spectra even for cosmologies with very blue power-law input spectra, for which SPT diverges. We compare predictions for the density and velocity divergence power spectra as well as the bispectrum at one-loop order to N-body results in a scaling universe with spectral indices $-1\leq n_s\leq +2$. We find a good agreement up to the non-linear scale for all cases, with a reach that increases with the spectral index $n_s$. We discuss the generation of vorticity as well as vector and tensor modes of the velocity dispersion, showing that neglecting vorticity when including dispersion would lead to a violation of momentum conservation. We verify momentum conservation when including vorticity, and compute the vorticity power spectrum at two-loop order, necessary to recover the correct large-scale limit with slope $n_w=2$. Comparing to our N-body measurements confirms the cross-over from $k^4$ to $k^2$ scaling on large scales. Our results provide a proof-of-principle that perturbative techniques for dark matter clustering can be systematically improved based on the known underlying collisionless dynamics.