The dark matter dispersion tensor in perturbation theory

TL;DR

This paper calculates the dark matter velocity dispersion tensor up to third order in perturbation theory, revealing growing solutions and their impact on the matter power spectrum, with implications for warm dark matter and neutrino clustering.

Contribution

It introduces a general third-order perturbative formalism for the dark matter velocity dispersion tensor, applicable to various perturbation approaches, and analyzes its effects on large-scale structure.

Findings

Velocity dispersion tensor exhibits growing solutions at third order.

Corrections to the matter power spectrum include EFT-like terms with quadratic growth.

Free-streaming scale suppresses the 1-loop power spectrum and shifts to larger scales.

Abstract

We compute the dark matter velocity dispersion tensor up to third order in perturbation theory using the Lagrangian formalism, revealing growing solutions at the third and higher orders. Our results are general and can be used for any other perturbative formalism. As an application, corrections to the matter power spectrum are calculated, and we find that some of them have the same structure as those in the effective field theory of large-scale structure, with "EFT-like" coefficients that grow quadratically with the linear growth function and are further suppressed by powers of the logarithmic linear growth factor $f$; other corrections present additional $k$ dependence. Due to the velocity dispersions, there exists a free-streaming scale that suppresses the whole 1-loop power spectrum. Furthermore, we find that as a consequence of the nonlinear evolution, the free-streaming length is shifted towards larger scales, wiping out more structure than that expected in linear theory. Therefore, we argue that the formalism developed here is better suited for a perturbation treatment of warm dark matter or neutrino clustering, where the velocity dispersion effects are well known to be important. We discuss implications related to the nature of dark matter.