The running spectral index as a probe of physics at high scales

The WMAP results on the scalar spectral index n and its running with scale, though preliminary, open a very interesting window to physics at very high energies. We address the problem of finding inflaton potentials well motivated by particle physics which can accommodate WMAP data. We make a model independent analysis of a large class of models: those with. at tree-level potentials lifted by radiative corrections, which cause the slow rolling of the inflaton and the running of n. This includes typical hybrid inflation models. In the small coupling regime the predictions for the size and running of n are remarkably neat, e. g. - dn/dlnk = (n - 1)(2) similar to << 1, and n does not cross n = 1, contrary to WMAP indications. On the other hand, n can run significantly if the couplings are stronger, but at the price of having a small number of e-folds, Ne. We also examine the effect of mass thresholds crossed during inflation. Finally, we show that the presence of non-renormalizable operators for the inflaton, suppressed by a mass scale above the inflationary range, is able to give both dn/dlnk similar to O(-0.05) and N-e similar to 50.