A closer look at dark matter production in exponential growth scenarios

TL;DR

This paper examines a non-thermal dark matter production mechanism involving exponential growth, testing the common equilibrium assumption by numerically solving the Boltzmann equation, and finds approximate equilibrium behavior at low momenta.

Contribution

It provides a numerical analysis of dark matter distribution evolution, challenging the assumption of equilibrium distribution during exponential growth phases.

Findings

Dark matter distribution shows equilibrium-like behavior at low momenta after growth stops.

The scaled equilibrium approximation estimates dark matter abundance reasonably well.

Full Boltzmann equation solutions are necessary for precise results.

Abstract

We investigate a recently proposed non-thermal mechanism for dark matter production, in which a small initial dark matter ($\chi$) number density undergoes exponential growth through scatterings with bath particles ($\phi$) in the early universe ($\chi \phi \to \chi \chi$). The process ends when the scattering rate becomes Boltzmann suppressed. The analysis, in literature, is performed on the simplifying assumption of the dark matter phase space tracing the equilibrium distribution of either standard model or a hidden sector bath. Owing to the non-thermal nature of the production mechanism, this assumption may not necessarily hold. In this work, we test the validity of this assumption by numerically solving the unintegrated Boltzmann equation for the dark matter distribution. Our results, independent of the initial conditions, show that after exponential growth ceases, the dark matter distribution exhibits equilibrium-like behaviour at low comoving momentum, especially for higher couplings. While full kinetic equilibrium-like behaviour is not reached across all momentum modes, the scaled equilibrium approximation provides reasonable estimates for the dark matter abundance. For more accurate results, however, the full unintegrated Boltzmann equation must be solved.