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Big-bang nucleosynthesis (BBN) is valuable as a means to constrain thephysics of the early universe and it is the only probe of theradiation-dominated epoch. A fundamental assumption in BBN is that the nuclearvelocity distributions obey Maxwell-Boltzmann (MB) statistics as they do instars. Specifically, the BBN epoch is characterized by a dilute baryon plasmafor which the velocity distribution of nuclei is mainly determined by thedominant Coulomb elastic scattering with mildly relativistic electrons. Onemust therefore deduce the momentum distribution for reacting nuclei from themulti-component relativistic Boltzmann equation. However, the fullmulti-component relativistic Boltzmann equation has only recently been analyzedand its solution has only been worked out in special cases. Moreover, a varietyof schemes have been proposed that introduce non-thermal components into theBBN 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-Carlosimulations which clarify the baryon distribution during BBN and can be used toanalyze any relaxation from a non-thermal injection. We show by these analysesthat the thermalization process leads to a nuclear distribution function thatremains very close to MB statistics even during the most relativisticenvironment relevant to BBN. Hence, the predictions of standard BBN remainunchanged.

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