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

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

Authors

Marvin Sipp, Hannes Heisler, Matthias Bartelmann

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 non-perturbative techniques are required to accurately capture the physics of cosmic structure formation.

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