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. We pay particular attention 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 constrain the properties of the power spectrum, they 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.

• Received 18 December 2011

DOI:https://doi.org/10.1103/PhysRevD.85.103533