What do WMAP and SDSS really tell about inflation?

Abstract

We derive new constraints on the Hubble function H(phi) and subsequently on the inflationary potential V(phi) from WMAP 3-year data combined with the Sloan Luminous Red Galaxy survey (SDSS-LRG), using a new methodology which appears to be more generic, conservative and model-independent than in most of the recent literature, since it depends neither on the slow-roll approximation, nor on any extrapolation scheme for the potential beyond the observable e-fold range, nor on additional assumptions about initial conditions for the inflaton velocity. This last feature represents the main improvement of this work, and is made possible by the reconstruction of H(phi) prior to V(phi). Our results only rely on the assumption that within the observable range, corresponding to ~ 10 e-folds, inflation is not interrupted and the function H(phi) is smooth enough for being Taylor-expanded at order one, two or three. We conclude that the variety of potentials allowed by the data is still large. However, it is clear that the first two slow-roll parameters are really small while the validity of the slow-roll expansion beyond them is not established.