Far-from-equilibrium kinetic dynamics of $\lambda \phi^4$ theory in an expanding universe

TL;DR

This paper studies the complex far-from-equilibrium dynamics of a massless scalar field with quartic interactions in an expanding universe, introducing a new analytical method for moments of the Boltzmann equation.

Contribution

It develops a covariant generating function approach to analyze the spectrum and moments of the Boltzmann collision operator for $mbda 4$ theory in curved spacetime.

Findings

Derived the spectrum and eigenfunctions of the linearized collision operator.

Established exact equations for moments in the nonlinear regime.

Compared numerical solutions for scalar field and hard sphere gases.

Abstract

We investigate the far-from-equilibrium behavior of the Boltzmann equation for a gas of massless scalar field particles with quartic (tree level) self-interactions ($\lambda \phi^4$) in Friedmann-Lemaitre-Robertson-Walker spacetime. Using a new covariant generating function for the moments of the Boltzmann distribution function, we analytically determine a subset of the spectrum and the corresponding eigenfunctions of the linearized Boltzmann collision operator. We show how the covariant generating function can be also used to find the exact equations for the moments in the full nonlinear regime. Different than the case of a ultrarelativistic gas of hard spheres (where the total cross section is constant), for $\lambda \phi^4$ the fact that the cross section decreases with energy implies that moments of arbitrarily high order directly couple to low order moments. Numerical solutions for the scalar field case are presented and compared to those found for a gas of hard spheres.