Recovering the inflationary potential and primordial power spectrum with a slow roll prior: methodology and application to WMAP three year data

We introduce a new method for applying an inflationary prior to a cosmological data set that includes relations between observables at arbitrary order in the slow roll expansion. The process is based on the inflationary flow equations, and the slow roll parameters appear explicitly in the cosmological parameter set. We contrast our method with other ways of imposing an inflationary prior on a cosmological data set, and argue that this method is ideal for use with heterogeneous data sets. In particular, it would be well suited to exploiting any direct detection of fundamental tensor modes by a BBO-style mission. To demonstrate the practical use of this method we apply it to the WMAPI + All data set, and the newly released WMAPII data set on its own and together with the SDSS data. We find that all basic classes of single field inflationary models are still allowed at the 1-2s level, but the overall parameter space is sharply constrained. In particular, we find evidence that the combination WMAPII + SDSS is sensitive to effects arising from terms that are quadratic in the two leading order slow roll parameters.