Recombination dynamics of primordial hydrogen and helium (He I) in the universe

We calculated the ionization fraction for hydrogen and helium (He I) as a function of the redshift z by including the two-photon decays of high hydrogen and parahelium levels and the radiative transfer in the helium 2 3 P 1 ↔ 1 1 S 0 intercombination line. We show that this yields corrections of no more than a few percent to the ionization fraction for hydrogen and speeds up significantly the recombination for helium compared to the recent works by Seager et al. (1999, 2000), in which these effects were disregarded.