Recent cosmic microwave background observations and the ionization history of the universe

Interest in nonstandard recombination scenarios has been spurred by recent cosmic microwave background (CMB) results from BOOMERANG and MAXIMA, which show an unexpectedly low second acoustic peak, resulting in a best-fit baryon density that is 50% larger than the prediction of big-bang nucleosynthesis (BBN). This apparent discrepancy can be avoided if the universe has a nonstandard ionization history in which the recombination of hydrogen is significantly delayed relative to the standard model. While future CMB observations may eliminate this discrepancy, it is useful to develop a general framework for analyzing nonstandard ionization histories. We develop such a framework, examining nonstandard models in which the hydrogen binding energy $E_b$ and the overall expression for the time rate of change of the ionized fraction of electrons are multiplied by arbitrary factors. This set of models includes a number of previously proposed models as special cases. We find a wide range of models with delayed recombination that are able to fit the CMB data with a baryon density in accordance with BBN, but there are even allowed models with earlier recombination than in the standard model. A generic prediction of these models is that the third acoustic CMB peak should be very low relative to what is found in the standard model. This is the case even for the models with earlier recombination than in the standard model, because here the third peak is lowered by an increased diffusion damping at recombination relative to the standard model. Interestingly, the specific height of the third peak depends sensitively on the model parameters, so that future CMB measurements will be able to distinguish between different nonstandard recombination scenarios.