On the coupling between different species during recombination

Measurements of fluctuations in the Cosmic Microwave Background Radiation (CMBR) is one of the most promising methods for measuring the fundamental cosmological parameters. However, in order to infer parameters from precision measurements it is necessary to calculate the theoretical fluctuation spectrum to at least the measurement accuracy. Standard treatments assume that electrons, ions and neutral hydrogen are very tightly coupled during the entire recombination history, and that the baryon-photon plasma can be treated as a two-fluid system consisting of baryons and photons interacting via Thomson scattering. We investigate the validity of this approximation by explicitly writing down and solving the full set of Boltzmann equations for electrons, ions, neutral hydrogen and photons. The main correction to the standard treatment is from including Rayleigh scattering between photons and neutral hydrogen, a change of less than 0.1% in the CMBR power spectrum. Our conclusion is thus that the standard treatment of the baryon-photon system is a very good approximation, better than any possible measurement accuracy.