Cosmological perturbation theory for large scale structure in phase space

TL;DR

This paper introduces a new perturbation theory framework for large scale structure that solves the Vlasov-Poisson system in phase space, relaxing assumptions of negligible velocity dispersion and connecting to effective field theory methods.

Contribution

It develops a comprehensive phase space perturbation theory for LSS, deriving standard kernels and naturally incorporating EFT counterterms.

Findings

Re-derivation of SPT kernels up to third order

Identification of EFT counterterms within the new framework

Highlighting the importance of modeling short-distance fluctuations

Abstract

We develop a framework for Large Scale Structure (LSS) perturbation theory, that solves the Vlasov-Poisson system of equations for the distribution function in full phase space. This approach relaxes the usual apriori assumption of negligible velocity dispersion underlying the Standard Perturbation Theory (SPT). We apply the new method to rederive the usual SPT kernels up to third order in the perturbative expansion. We also show that a counterterm, identical to the one introduced by standard Effective Field Theory (EFT) methods, naturally arises within our framework. We finish by making a precise connection to EFT techniques, which reveals the necessity of the EFTofLSS to self-consistently model the long-wavelength fluid, and illustrates the importance of having theoretical control over short distance fluctuations.