The Thermal Abundance of Semi-Relativistic Relics

TL;DR

This paper introduces a semi-analytical method to calculate relic densities of semi-relativistic particles, like neutrinos, which are neither fully relativistic nor non-relativistic at decoupling, revealing their limited role as cold dark matter.

Contribution

It proposes a new ansatz for thermal averages of annihilation cross sections, enabling relic density calculations for semi-relativistic particles, filling a gap in existing analytical solutions.

Findings

Semi-relativistic relics are unsuitable as cold dark matter candidates.

Late decays of such relics can dilute unwanted relic densities.

The method applies to Majorana and Dirac neutrinos.

Abstract

Approximate analytical solutions of the Boltzmann equation for particles that are either extremely relativistic or non-relativistic when they decouple from the thermal bath are well established. However, no analytical formula for the relic density of particles that are semi-relativistic at decoupling is yet known. We propose a new ansatz for the thermal average of the annihilation cross sections for such particles, and find a semi-analytical treatment for calculating their relic densities. As examples, we consider Majorana- and Dirac-type neutrinos. We show that such semi-relativistic relics cannot be good cold Dark Matter candidates. However, late decays of meta-stable semi-relativistic relics might have released a large amount of entropy, thereby diluting the density of other, unwanted relics.