Cosmic structure from the path integral of classical mechanics and its comparison to standard perturbation theory

TL;DR

This paper develops a path-integral approach to cosmic structure formation, reproduces standard perturbation theory results with a new initial condition sampling method, and highlights the need for nonperturbative techniques for accurate modeling.

Contribution

It introduces Resummed Kinetic Field Theory with a novel initial sampling method, aligning results with standard perturbation theory and emphasizing the importance of nonperturbative approaches.

Findings

Exact reproduction of one-loop SPT results using new sampling method

Deviations in previous methods attributed to sampling inconsistencies

Full phase-space approach indicates need for nonperturbative techniques

Abstract

We investigate cosmic structure formation in the framework of a path-integral formulation of an $N$-particle ensemble in phase space, dubbed Resummed Kinetic Field Theory (RKFT), up to one-loop perturbative order. In particular, we compute power spectra of the density contrast, the divergence and curl of the momentum density and arbitrary $n$-point cumulants of the stress tensor. In contrast to earlier works, we propose a different method of sampling initial conditions, with a Gaussian initial phase-space density. Doing so, we exactly reproduce the corresponding results from Eulerian standard perturbation theory (SPT) at one-loop order, showing that formerly found deviations can be fully attributed to inconsistencies in the previous sampling method. Since, in contrast to SPT, the full phase-space description does not assume a truncation of the Vlasov hierarchy, our findings suggest that nonperturbative techniques are required to accurately capture the physics of cosmic structure formation.