# Saha ionization equation in early universe

## TL;DR

This paper examines the ionization equilibrium of hydrogen in the early universe using thermal field theory, comparing ionization-recombination rates with cosmic expansion to understand matter-radiation interactions.

## Contribution

It introduces a real-time thermal field theory approach to calculate hydrogen ionization and recombination rates in the early universe, focusing on ground state atoms.

## Key findings

- Calculated ionization-recombination rate differences
- Compared rates with universe expansion at various temperatures
- Provided insights into hydrogen atom equilibration in the early universe

## Abstract

The Saha equation follows from thermal equilibrium of matter and radiation. We discuss this problem of equilibrium in the early universe, when matter consists mostly of electrons, protons and hydrogen atoms. Taking H-atoms in their ground state only and applying the real time formulation of thermal field theory, we calculate the difference of ionization and recombination rates, which controls the equilibration of H-atoms. This rate is compared with the expansion rate of the universe at different temperatures.