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