Dynamical equation for the degree of ionization of the cosmic substratum before the formation of the galaxy

The variable degree of ionization x of a hydrogen-helium plasma in the early universe for a quasi-static expansion in thermal equilibrium is discussed. The final equation for the degree of ionization can be reduced to a polynomial of fourth order in x with known coefficients, depending on the temperature. Restricting this investigation to a pure hydrogen-plasma applied to the recombination era, where the main ionization effects are due to photoelectric and collisional processes, the dynamical evolution of the degree of ionization for nonstatic and nonequilibrium situations is studied. The calculation can be reduced to a pure quadrature. In the linear case, the rate of ionization is also calculated. (Author)