Statistical mechanics and the description of the early universe II. Principle of detailed balance and primordial 4He formation

TL;DR

This paper investigates how slight non-extensivity in the early universe's statistical mechanics affects primordial element formation, especially helium and deuterium, by introducing corrections to the principle of detailed balance and analyzing their impact on nucleosynthesis.

Contribution

It introduces a non-extensive correction to the principle of detailed balance and analytically studies its effects on primordial nucleosynthesis, including neutron decay and element yields.

Findings

Non-extensive corrections modify helium and deuterium formation.

The correction to the capture time influences neutron decay modeling.

New bounds on the non-extensive parameter are derived from observational data.

Abstract

If the universe is slightly non-extensive, and the distribution functions are not exactly given by those of Boltzmann-Gibbs, the primordial production of light elements will be non-trivially modified. In particular, the principle of detailed balance (PDB), of fundamental importance in the standard analytical analysis, is no longer valid, and a non-extensive correction appears. This correction is computed and its influence is studied and compared with previous works, where, even when the universe was considered as an slightly non-extensive system, the PDB was assumed valid. We analytically track the formation of Helium and Deuterium, and study the kind of deviation one could expect from the standard regime. The correction to the capture time, the moment in which Deuterium can no longer be substantially photo-disintegrated, is also presented. This allows us to take into account the process of the free decay of neutrons, which was absent in all previous treatments of the topic. We show that even when considering a first (linear) order correction in the quantum distribution functions, the final output on the primordial nucleosynthesis yields cannot be reduced to a linear correction in the abundances. We finally obtain new bounds upon the non-extensive parameter, both comparing the range of physical viability of the theory, and using the latest observational data.