Unitarity limits on thermal dark matter in (non-)standard cosmologies

TL;DR

This paper derives upper bounds on dark matter particle masses based on unitarity limits of inelastic reactions, considering various cosmological scenarios and number-changing processes, providing constraints on thermal dark matter models.

Contribution

It introduces a general framework for calculating maximum dark matter masses from unitarity bounds for k→2 reactions across different cosmologies.

Findings

Maximum DM mass for s-wave annihilation is about 130 TeV in standard cosmology.

Reheating temperatures above certain thresholds are disfavored for specific reaction orders.

Constraints vary significantly with the number of particles involved in the annihilation process.

Abstract

Using the upper bound on the inelastic reaction cross-section implied by S-matrix unitarity, we derive the thermally averaged maximum dark matter (DM) annihilation rate for general $k \rightarrow 2$ number-changing reactions, with $k \geq 2$, taking place either entirely within the dark sector, or involving standard model fields. This translates to a maximum mass of the particle saturating the observed DM abundance, which, for dominantly $s$-wave annihilations, is obtained to be around $130$ TeV, $1$ GeV, $7$ MeV and $110$ keV, for $k=2,3,4$ and $5$, respectively, in a radiation dominated Universe, for a real or complex scalar DM stabilized by a minimal symmetry. For modified thermal histories in the pre-big bang nucleosynthesis era, with an intermediate period of matter domination, values of reheating temperature higher than $\mathcal{O}(200)$ GeV for $k \geq 4$, $\mathcal{O}(1)$ TeV for $k=3$ and $\mathcal{O}(50)$ TeV for $k=2$ are strongly disfavoured by the combined requirements of unitarity and DM relic abundance, for DM freeze-out before reheating.