Interaction rates in cosmology: heavy particle production and scattering

TL;DR

This paper develops a new method to calculate particle interaction rates in an expanding universe, revealing effects like Lorentz invariance violation, freeze-out, and sub-threshold production that impact dark matter abundance.

Contribution

It introduces an adiabatic expansion approach for transition rates in cosmology, addressing limitations of the S-matrix formulation in a rapidly expanding universe.

Findings

Violation of local Lorentz invariance due to cosmological redshift

Freeze-out of production cross sections at finite times

Sub-threshold production of heavier particles enhances dark matter abundance

Abstract

We study transition rates and cross sections from first principles in a spatially flat radiation dominated cosmology. We consider a model of scalar particles to study scattering and heavy particle production from pair annihilation, drawing more general conclusions. The S-matrix formulation is ill suited to study these ubiquitous processes in a rapidly expanding cosmology. We introduce a physically motivated adiabatic expansion that relies on wavelengths much smaller than the particle horizon at a given time. The leading order in this expansion dominates the transition rates and cross sections. Several important and general results are direct consequences of the cosmological redshift and a finite particle horizon: i) a violation of local Lorentz invariance, ii) freeze-out of the production cross section at a finite time, iii) sub-threshold production of heavier particles as a consequence of the uncertainty in the local energy from a finite particle horizon, a manifestation of the \emph{antizeno} effect. If heavy dark matter is produced via annihilation of a lighter species, sub-threshold production yields an enhanced abundance. We discuss several possible consequences of these effects.