2.4. Complex ionization history
The full ionization history of the Universe is given by specifying the ionization fraction as a function of redshift z. The simplest scenario takes the ionization to be zero from recombination up to some redshift zion, at which point the Universe instantaneously re-ionizes completely. In that case, there is a one-to-one correspondence between and zion (that relation, however, also depending on other cosmological parameters).
While simple models of the re-ionization process suggest that rapid ionization is a good approximation, observational evidence is mixed, as it is difficult to reconcile the high optical depth inferred from the microwave background with absorption seen in some high-redshift quasar systems, and also perhaps with the temperature of the intergalactic medium at z 3. Accordingly, a more complex ionization history may need to be considered, and perhaps separate histories for hydrogen and helium, which will necessitate new parameters. Additionally, high-precision microwave anisotropy experiments may require consideration of the level of residual ionization left after recombination, which in principle is computable from the other cosmological parameters.