Revisiting Dark Matter Freeze-in and Freeze-out through Phase-Space Distribution

TL;DR

This paper analyzes dark matter production mechanisms by solving phase-space Boltzmann equations, revealing significant differences from traditional methods and highlighting the impact of non-thermal distributions on cosmic structure formation.

Contribution

It introduces a phase-space distribution approach to dark matter relic abundance calculations, showing notable deviations from number-density methods and exploring effects of non-thermal distributions and elastic scatterings.

Findings

Significant differences between phase-space and number-density approaches in the transition regime.

Non-thermal and multi-modal phase-space distributions can arise from freeze-in and freeze-out processes.

Elastic scatterings can distort non-thermal distributions, affecting structure formation.

Abstract

We revisit dark-matter production through freeze-in and freeze-out by solving the Boltzmann equations at the level of the phase-space distribution $f(p,t)$. Using the $2\to2$ annihilation and the $1\to2$ decay processes for illustration, we compare the resulting dark-matter relic abundance with that from the number-density approach. In the transition regime between freeze-in and freeze-out, we find the difference can be quite significant, or even by orders of magnitude if the annihilation of dark-matter particles or the decaying mediator is neglected. The freeze-in production in the $2\to2$ and the $1\to 2$ processes can also result in non-thermal phase-space distributions, or even multi-modal ones with out-of-equilibrium decay, which can potentially affect structure formation at late times. We also investigate how elastic scatterings can distort such non-thermal distributions.