New constraints on the observable inflaton potential from WMAP and SDSS

We derive some new constraints on single-field inflation from the Wilkinson Microwave Anisotropy Probe 3-year data combined with the Sloan Luminous Red Galaxy survey. Our work differs from previous analyses by focusing only on the observable part of the inflaton potential, or in other words, by making absolutely no assumption about extrapolation of the potential from its observable region to its minimum (i.e., about the branch of the potential responsible for the last ~50 inflationary e-folds). We only assume that inflation starts at least a few e-folds before the observable Universe leaves the Hubble radius, and that the inflaton rolls down a monotonic and regular potential, with no sharp features or phase transitions. We Taylor-expand the inflaton potential at order v=2, 3 or 4 in the vicinity of the pivot scale, compute the primordial spectra of scalar and tensor perturbations numerically and fit the data. For v>2, a large fraction of the allowed models is found to produce a large negative running of the scalar tilt, and to fall in a region of parameter space where the second-order slow-roll formalism is strongly inaccurate. We release a code for the computation of inflationary perturbations which is compatible with CosmoMC.