Vlasov Perturbation Theory and the role of higher cumulants

TL;DR

This paper introduces a new Vlasov Perturbation Theory that incorporates higher cumulants of the phase-space distribution, improving the understanding of collisionless dark matter dynamics in cosmology.

Contribution

The authors develop a high-order cumulant hierarchy approach to Vlasov Perturbation Theory, extending beyond standard perturbation theory and analyzing its impact on cosmological structure formation.

Findings

Higher cumulants have minor effects on power spectra at weakly non-linear scales.

Spurious exponential growth is eliminated under certain scalar-mode constraints.

Loop corrections in VPT are finite for hierarchical initial spectra.

Abstract

We develop a new approach to Vlasov Perturbation Theory (VPT) that solves for the hierarchy of cumulants of the phase-space distribution function to arbitrarily high truncation order in the context of cosmological structure formation driven by collisionless dark matter. We investigate the impact of higher cumulants on density and velocity power spectra as well as the bispectrum, and compare to scale-free $N$-body simulations. While there is a strong difference between truncation at the first cumulant, i.e. standard perturbation theory (SPT), and truncation at the second (i.e. including the velocity dispersion tensor), the third cumulant has a small quantitative impact and fourth and higher cumulants only have a minor effect on these summary statistics at weakly non-linear scales. We show that spurious exponential growth is absent in vector and tensor modes if scalar-mode constraints on the non-Gaussianity of the background distribution function that results from shell-crossing are satisfied, guaranteeing the screening of UV modes for all fluctuations of any type, as expected physically. We also show analytically that loop corrections to the power spectrum are finite within VPT for any initial power spectra consistent with hierarchical clustering, unlike SPT. Finally, we discuss the relation to and contrast our predictions with effective field theory (EFT), and discuss how the advantages of VPT and EFT approaches could be combined.