https://doi.org/10.1140/epjc/s10052-022-10003-x
Regular Article - Theoretical Physics
Non-Gaussian effects of the Saha’s ionization in the early universe
1
Departamento de Física, Universidade do Estado do Rio Grande do Norte, 59610-210, Mossoró, RN, Brazil
2
Departamento de Física, Universidade Federal da Paraíba, 58059-970, João Pessoa, PB, Brazil
3
Departamento de Ciências Exatas e Naturais, Universidade Federal Rural do Semi-Árido, 59900-000, Pau dos Ferros, RN, Brazil
Received:
6
October
2021
Accepted:
8
January
2022
Published online:
19
January
2022
Tsallis’ thermostatistical has received increasing attention due to its success in describing phenomena that manifest unusual thermodynamic properties. In this context, the generalized Saha equation must follow a condition of generalized thermal equilibrium of matter and radiation. The present work aims to explore the non-Gaussian effects on Saha’s ionization via Tsallis statistics. To accomplish this, we generalized the number density taking into account a non-Gaussian Fermi-Dirac distribution and then set out the Saha equation for the cosmological recombination. As a result, we highlight two new non-Gaussian effects: (i) two generalized chemical equilibrium conditions, one for the relativistic regime and the other for the non-relativistic one; and (ii) the hydrogen binding q-energy. We demonstrated that to yield smooth shifts in the binding energy, the a-parameter must be very small. We also showed that binding q-energy exhibits symmetrical behavior around the value of the standard binding energy. Besides, we used the q-energy in order to access other hydrogen energy levels, and we ascertained the values of the a-parameter that access those levels and their relationship to temperature. Finally, we employed these results to examine the non-Gaussian effects of the deuterium bottleneck, recombination, and the particle anti-particle excess.
© The Author(s) 2022
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