Non-Gaussian Effects of Saha Ionization in Cosmology and Gravitation
Equation of Saha; Tsallis's statistics; Rindler's space; primordial universe
Tsallis's non-Gaussian thermostatistics has received increasing attention due to its success in describing phenomena that manifest unusual thermodynamic properties. In this context, the non-Gaussian Saha equation must follow a generalized thermal equilibrium condition of matter and radiation. In this work, we intend to evaluate the non-Gaussian effects of Saha ionization in the domain of cosmology and gravitation. Specifically, we will emphasize the study of the primordial universe: cosmological recombination, Big Bang nucleosynthesis, and particle anti-particle excess. Furthermore, we will study the photoionization of hydrogen atoms and the production of electron-positron pairs, both in Rindler spacetime. As preliminary results, in cosmology, we highlight two important non-Gaussian effects: i) new conditions of chemical equilibrium, both for relativistic and non-relativistic regimes; and ii) new binding energy of the hydrogen atom. We also show that there is a q value other than 1 that gives the same result as the usual case for the nucleosynthesis temperature and the equilibrium fractional ionization temperature. In gravitation, we show that the non-Gaussian Saha equation in Rindler spacetime provides binding energy with a quadratic dependence of the gravitational field, whereas the usual result is a linear dependence. Therefore, the photoionization of hydrogen atoms and the production of pairs are both more intensely suppressed in regions with a strong gravitational field. Besides, we derive constraints on the gravitational field and the chemical potentials of the electron and positron.