Bayesian Analysis of Inflation II: Model Selection and Constraints on
  Reheating
  We discuss the model selection problem for inflationary cosmology. We couple
ModeCode, a publicly-available numerical solver for the primordial perturbation
spectra, to the nested sampler MultiNest, in order to efficiently compute
Bayesian evidence. Particular attention is paid to the specification of
physically realistic priors, including the parametrization of the
post-inflationary expansion and associated thermalization scale. It is
confirmed that while present-day data tightly constrains the properties of the
power spectrum, it cannot usefully distinguish between the members of a large
class of simple inflationary models. We also compute evidence using a simulated
Planck likelihood, showing that while Planck will have more power than WMAP to
discriminate between inflationary models, it will not definitively address the
inflationary model selection problem on its own. However, Planck will place
very tight constraints on any model with more than one observationally-distinct
inflationary regime -- e.g. the large- and small-field limits of the hilltop
inflation model -- and put useful limits on different reheating scenarios for a
given model.
