Non-equilibrium statistical field theory for classical particles: Non-linear structure evolution with first-order interaction

TL;DR

This paper develops a non-equilibrium statistical field theory approach for classical particles to model non-linear structure formation in cosmology, successfully reproducing the non-linear power spectrum evolution observed in simulations.

Contribution

It introduces a novel method that transports initial phase-space distributions without perturbing dynamical equations, capturing non-linear growth at first order in interaction.

Findings

Reproduces non-linear power spectrum up to redshift zero

Matches large wave number asymptotic behavior

Allows high density contrast at first order

Abstract

We calculate the power spectrum of density fluctuations in the statistical non-equilibrium field theory for classical, microscopic degrees of freedom to first order in the interaction potential. We specialise our result to cosmology by choosing appropriate initial conditions and propagators and show that the non-linear growth of the density power spectrum found in numerical simulations of cosmic structure evolution is reproduced well to redshift zero and for arbitrary wave numbers. The main difference of our approach to ordinary cosmological perturbation theory is that we do not perturb a dynamical equation for the density contrast. Rather, we transport the initial phase-space distribution of a canonical particle ensemble forward in time and extract any collective information from it at the time needed. Since even small perturbations of particle trajectories can lead to large fluctuations in density, our approach allows to reach high density contrast already at first order in the perturbations of the particle trajectories. We argue why the expected asymptotic behaviour of the non-linear power spectrum at large wave numbers can be reproduced in our approach at any order of the perturbation series.