Slow Roll Reconstruction: Constraints on Inflation from the 3 Year WMAP Dataset

We study the constraints on the inflationary parameter space derived from the 3 year WMAP dataset using ``slow roll reconstruction, using the SDSS galaxy power spectrum to gain further leverage where appropriate. This approach inserts the inflationary slow roll parameters directly into a Monte Carlo Markov chain estimate of the cosmological parameters, and uses the inflationary flow hierarchy to compute the parameters scale-dependence. We work with the first three parameters (epsilon, eta and xi) and pay close attention to the possibility that the 3 year WMAP dataset contains evidence for a ``running spectral index, which is dominated by the xi term. Mirroring the WMAP teams analysis we find that the permitted distribution of xi is broad, and centered away from zero. However, when we require that inflationary parameters yield at least 30 additional e-folds of inflation after the largest observable scales leave the horizon, the bounds on xi tighten dramatically. We make use of the absence of an explicit pivot scale in the slow roll reconstruction formalism to determine the dependence of the computed parameter distributions on the pivot. We show that the choice of pivot has a significant effect on the inferred constraints on the inflationary variables, and the spectral index and running derived from them. Finally, we argue that the next round of cosmological data can be expected to place very stringent constraints on the region of parameter space open to single field models of slow roll inflation.