Analysis of the Multi-component Relativistic Boltzmann Equation for Electron Scattering in Big Bang Nucleosynthesis

TL;DR

This paper derives and analyzes the multi-component relativistic Boltzmann equation for nuclei in Big Bang Nucleosynthesis, demonstrating that thermalization maintains Maxwell-Boltzmann distributions, thus supporting standard BBN predictions.

Contribution

The paper constructs the relativistic Boltzmann equation for BBN, derives a Langevin model, and uses Monte-Carlo simulations to show thermalization preserves Maxwell-Boltzmann distributions.

Findings

Nuclear distributions remain close to Maxwell-Boltzmann during BBN.

Thermalization processes do not significantly alter standard BBN predictions.

Relativistic Monte-Carlo simulations confirm the robustness of thermal distributions.

Abstract

Big-bang nucleosynthesis (BBN) is valuable as a means to constrain the physics of the early universe and it is the only probe of the radiation-dominated epoch. A fundamental assumption in BBN is that the nuclear velocity distributions obey Maxwell-Boltzmann (MB) statistics as they do in stars. Specifically, the BBN epoch is characterized by a dilute baryon plasma for which the velocity distribution of nuclei is mainly determined by the dominant Coulomb elastic scattering with mildly relativistic electrons. One must therefore deduce the momentum distribution for reacting nuclei from the multi-component relativistic Boltzmann equation. However, the full multi-component relativistic Boltzmann equation has only recently been analyzed and its solution has only been worked out in special cases. Moreover, a variety of schemes have been proposed that introduce non-thermal components into the BBN environment which can alter the thermal distribution of reacting nuclei. Here, we construct the relativistic Boltzmann equation in the context of BBN. We also derive a Langevin model and perform relativistic Monte-Carlo simulations which clarify the baryon distribution during BBN and can be used to analyze any relaxation from a non-thermal injection. We show by these analyses that the thermalization process leads to a nuclear distribution function that remains very close to MB statistics even during the most relativistic environment relevant to BBN. Hence, the predictions of standard BBN remain unchanged.