Verification of Maxwell-Boltzmann distribution with Big-Bang Nucleosyntheis theory

TL;DR

This study verifies the Maxwell-Boltzmann distribution's validity in Big-Bang Nucleosynthesis by analyzing the impact of non-extensive statistics, finding only minimal deviations are permissible for the classical distribution.

Contribution

First, it assesses the effect of non-extensive Tsallis statistics on thermonuclear reaction rates in BBN; second, it confirms the Maxwell-Boltzmann distribution's microscopic validity within BBN.

Findings

Reverse reaction rates are highly sensitive to the non-extensive q parameter.

Only a tiny deviation of ±6×10^{-4} from MB distribution is allowed based on primordial abundance observations.

Classical Maxwell-Boltzmann statistics are validated within the BBN environment.

Abstract

The current Big-Bang Nucleosynthesis (BBN) model has been constructed based on a nuclear reaction network operating with thermal reactivities of Maxwell-Boltzmann (MB) distribution plasma. However, does the classical MB distribution still hold for the extremely high-temperature (in order of 10$^9$ K) plasma involved in the Big-Bang environment? In this work, we have investigated the impact of non-extensive Tsallis statistics (in $q$-Guassian distribution) on the thermonuclear reaction rates. We show for the first time that the reverse rates are extremely sensitive to the non-extensive $q$ parameter. Such sensitivity does not allow a large deviation of non-extensive distribution from the usual MB distribution. With a newly developed BBN code, the impact of primordial light-element abundances on $q$ values has been studied by utilizing the most recent BBN cosmological parameters and the available nuclear cross-section data. For the first time, we have accurately verified the microscopic MB distribution with the macroscopic BBN theory and bservation. By comparing the recent observed primordial abundances with our predictions, only a tiny deviation of $\pm$6$\times$10$^{-4}$ at most can be allowed for the MB distribution. However, validity of the classical statistics needs to be studied further for the self-gravitating stars and binaries of high-density environment, with the extreme sensitivity of reverse rate on $q$ found here.