A new calculation of the recombination epoch

We have developed an improved recombination calculation of H, He I, and He II in the early universe that involves a line-by-line treatment of each atomic level. We find two major differences compared with previous calculations. First, the ionization fraction x(e) is approximately 10% smaller for redshifts less than or similar to 800 because of nonequilibrium processes in the excited states of H. Second, He I recombination is much slower than previously thought, and it is delayed until just before H recombines. We describe the basic physics behind the new results and present a simple way to reproduce our calculation. This should enable a fast computation of the ionization history (and of the quantities such as the power spectrum of cosmic microwave background anisotropies that depend on it) for arbitrary cosmologies, without the need to consider the hundreds of atomic levels used in our complete model.