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 accomodate WMAP data .
We make a model independent analysis of a large class of models : those with flat tree-level potential 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 / d \ln k = ( n - 1 ) ^ { 2 } \ll 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 , N _ { e } .
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 / d \ln k \sim { \cal O } ( -0.05 ) and N _ { e } \sim 50 .