Quantum Kinetic Equations and Dark Matter Abundances Reconsidered

TL;DR

This paper reevaluates the derivation of quantum kinetic equations for dark matter relic densities, arguing that the conventional Boltzmann equation remains valid over recent modified versions that include virtual particle effects.

Contribution

It critically assesses a recent modification to the quantum Boltzmann equation, demonstrating that the standard form correctly accounts for interaction energies in dark matter calculations.

Findings

The modified Boltzmann equation overestimates relic densities.

The conventional Boltzmann equation accurately describes particle interactions.

Virtual particle effects do not significantly alter dark matter abundance calculations.

Abstract

Starting from a Caldeira-Leggett model for the interaction of a system with an environment, Joichi, Matsumoto, and Yoshimura have reconsidered the derivation of the quantum Boltzmann equation. They find an extra term that accounts for the effects of virtual particles, and which drastically changes the results for relic densities of stable, weakly interacting massive particles (WIMPs), and for the decay products of unstable particles. We show, however, that this modified Boltzmann equation does not properly account for the interaction energy between the massive particles (which are decaying or annihilating) and the thermal bath of light particles. We argue that the conventional Boltzmann equation gives the correct result.