Boltzmann equation and its cosmological applications

TL;DR

This paper reviews the derivation of the Boltzmann equation from quantum field theory and explores its key cosmological applications, including dark matter dynamics and baryogenesis, emphasizing detailed collision term analysis and temperature extensions.

Contribution

It provides a detailed derivation of the Boltzmann equation without assuming finite temperature systems and discusses its applications in cosmology, especially in dark matter and baryogenesis scenarios.

Findings

Detailed derivation of the Boltzmann equation from quantum field theory.

Extension of the Boltzmann equation to include temperature parameters.

Application of the equation to dark matter freeze-out/in and baryogenesis processes.

Abstract

We review the derivation of the Boltzmann equation and its cosmological applications in this paper. The derivation of the Boltzmann equation, especially the collision term, is discussed in detail in the language of the quantum field theory without any assumption of the finite temperature system. We also discuss the integrated Boltzmann equation with the deal of the temperature parameter as an extension of the standard equation. Among a number of its cosmological applications, we mainly target two familiar examples, the dynamics of the dark matter abundance through the freeze-out/in process and a baryogenesis scenario. The formulations in those systems are briefly discussed with techniques in their calculations.