Regular Article - Theoretical Physics
Non-Gaussian effects of the Saha’s ionization in the early universe
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
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
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
Funded by SCOAP3