What do WMAP and SDSS really tell us about inflation?

Abstract

We derive new constraints on the Hubble functionH(ϕ) and subsequently on the inflationary potentialV (ϕ) 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 andmodel independent than in most of the recent literature, since it depends not on theslow-roll approximation for computing the primordial spectra, or on any extrapolationscheme for the potential beyond the observable e-fold range, or on additional assumptionsabout initial conditions for the inflaton velocity. This last feature represents themain improvement of this work, and is made possible by the reconstruction ofH(ϕ) priorto V (ϕ). Our results only rely on the assumption that within the observable range, corresponding to∼10 e-folds, inflation is not interrupted and the functionH(ϕ) is smooth enough for being Taylor expanded at order one, two or three. We conclude thatthe variety of potentials allowed by the data is still large. However, it is clear that the firsttwo slow-roll parameters are really small while the validity of the slow-roll expansionbeyond them is not established.