Big-Bang Nucleosynthesis verifies classical Maxwell-Boltzmann distribution

TL;DR

This paper constrains deviations from the Maxwell-Boltzmann distribution in Big-Bang Nucleosynthesis, showing that non-extensive statistics must be very close to classical to match observed primordial abundances, with implications for astrophysics.

Contribution

It provides the most stringent limit on non-extensive statistical deviations in BBN, highlighting the sensitivity of reaction rates to the parameter q.

Findings

Deviations from Maxwell-Boltzmann are constrained to |δq|=6×10^{-4}.

Endothermic reaction rates are highly sensitive to q.

Non-extensive effects could influence heavy element nucleosynthesis.

Abstract

We provide the most stringent constraint to date on possible deviations from the usually-assumed Maxwell-Boltzmann (MB) velocity distribution for nuclei in the Big-Bang plasma. The impact of non-extensive Tsallis statistics on thermonuclear reaction rates involved in standard models of Big-Bang Nucleosynthesis (BBN) has been investigated. We find that the non-extensive parameter $q$ may deviate by, at most, $|\delta q|$=6$\times$10$^{-4}$ from unity for BBN predictions to be consistent with observed primordial abundances; $q$=1 represents the classical Boltzmann-Gibbs statistics. This constraint arises primarily from the {\em super}sensitivity of endothermic rates on the value of $q$, which is found for the first time. As such, the implications of non-extensive statistics in other astrophysical environments should be explored. This may offer new insight into the nucleosynthesis of heavy elements.