An Exact Solution of Riccati Form of Boltzmann Equation with Mathematica

Abstract

The Boltzmann equation is often used to calculate relic density of non-baryonic dark matter. The main idea is that particles were in thermal equilibrium with the early universe. There are many solutions for Boltzmann equation in the form of software packages, such as MadDM. This paper discusses an exact computational solution of Riccati form of Boltzmann equation with Mathematica. While in literature there is already another presentation of Mathematica routine to compute relic density, to our best knowledge, this solution has never been presented elsewhere before.