Energy Spectrum of Thermalizing High Energy Decay Products in the Early Universe

TL;DR

This paper analyzes the energy spectrum of decay products in the early universe, accounting for thermal effects and multiple scattering suppression, providing numerical solutions and analytical fits to the Boltzmann equation.

Contribution

It introduces a detailed numerical and analytical study of the decay product spectrum considering IR cutoff and LPM suppression in the early universe.

Findings

Derived an accurate analytical fit for the energy spectrum.

Quantified the impact of IR cutoff and LPM effect on thermalization.

Provided numerical solutions to the Boltzmann equation for decay products.

Abstract

We revisit the Boltzmann equation governing the spectrum of energetic particles originating from the decay of massive progenitors during the process of thermalization. We assume that these decays occur when the background temperature $T$ is much less than the mass $M$ of the progenitor. We pay special attention to the IR cutoff provided by the thermal bath, and include the suppression resulting from the interference of multiple scattering reactions (LPM effect). We solve the resulting integral equation numerically, and construct an accurate analytical fit of the solutions.