Saha ionization equation in 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.