Planck and re-ionization history: a model selection view

We use Bayesian model selection tools to forecast the Planck satellite's ability to distinguish between different models for the re-ionization history of the Universe, using the large angular scale signal in the cosmic microwave background polarization spectrum. We find that Planck is not expected to be able to distinguish between an instantaneous re-ionization model and a two-parameter smooth re-ionization model, except for extreme values of the additional re-ionization parameter. If it cannot, then it will be unable to distinguish between different two-parameter models either. However, Bayesian model averaging will be needed to obtain unbiased estimates of the optical depth to re-ionization. We also generalize our results to a hypothetical future cosmic variance limited microwave anisotropy survey, where the outlook is more optimistic.