Bayesian analysis of inflation. III. Slow roll reconstruction using model selection

We implement slow roll reconstruction---an optimal solution to the inverse problem for inflationary cosmology---within ModeCode, a publicly available solver for the inflationary dynamics. We obtain up-to-date constraints on the reconstructed inflationary potential, derived from the WMAP 7 year data set and South Pole Telescope observations, combined with large scale structure data derived from SDSS Data Release 7. Using ModeCode in conjunction with the MultiNest sampler, we compute Bayesian evidence for the reconstructed potential at each order in the truncated slow roll hierarchy. We find that the data are well-described by the first two slow roll parameters, $ϵ$ and η, and that there is no need to include a nontrivial ξ parameter.