Analysis of the multicomponent 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 multicomponent relativistic Boltzmann equation. However, the full multicomponent 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 nonthermal 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 nonthermal 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.

Figure 1

Monte-Carlo histograms (blue bars) of the kinetic energy distribution of baryons scattering in a bath of mildly relativistic FD $e^{+}-e^{-}$ plasma (black line) at $\mathrm{kT}=0.1\mathrm{MeV}$ (upper panel) and $\mathrm{kT}=0.01\mathrm{MeV}$ (lower panel) compared to the kinetic energy distribution of a classical Maxwell-Boltzmann distribution (red line).