Kinetic vs. Thermal-Field-Theory Approach to Cosmological Perturbations

TL;DR

This paper compares kinetic theory and thermal-field-theory approaches to modeling linear cosmological perturbations, showing their equivalence in high-temperature, collisionless, massless matter scenarios and analyzing initial data dependence.

Contribution

It provides a detailed comparison between kinetic and thermal-field-theory methods for cosmological perturbations, including analytical solutions and initial data effects.

Findings

Thermal-field-theory approach matches kinetic theory in high-temperature limit.

Analytical solutions for all singular and regular cases are derived.

Perturbation dependence on initial conditions is thoroughly analyzed.

Abstract

A closed set of equations for the evolution of linear perturbations of homogeneous, isotropic cosmological models can be obtained in various ways. The simplest approach is to assume a macroscopic equation of state, e.g.\ that of a perfect fluid. For a more refined description of the early universe, a microscopic treatment is required. The purpose of this paper is to compare the approach based on classical kinetic theory to the more recent thermal-field-theory approach. It is shown that in the high-temperature limit the latter describes cosmological perturbations supported by collisionless, massless matter, wherein it is equivalent to the kinetic theory approach. The dependence of the perturbations in a system of a collisionless gas and a perfect fluid on the initial data is discussed in some detail. All singular and regular solutions are found analytically.