Higgs inflation at the hilltop

We study inflation with the non-minimally coupled Standard Model Higgs in the case when quantum corrections generate a hilltop in the potential. We consider both the metric and the Palatini formulation of general relativity. We investigate hilltop inflation in different parts of the Higgs potential and calculate predictions for CMB observables. We run the renormalization group equations up from the electroweak scale and down from the hilltop, adding a jump in-between to account for unknown corrections in the intermediate regime. Within our approximation, no viable hilltop inflation is possible for small field values, where the non-minimal coupling has no role, nor for intermediate field values. For large field values, hilltop inflation works. We find the spectral index to be n(s) <= 0.96 in both the metric and the Palatini formulation, the upper bound coinciding with the tree-level result. The tensor-to-scalar ratio is r <= 1.2 x 10(-3) in the metric case and r <= 2.2 x 10(-9) in the Palatini case. Successful inflation is possible even when the renormalization group running is continuous with no jumps. In the metric formulation, r is smaller than in Higgs inflation on the tree-level plateau or at the critical point, making it possible to distinguish hilltop inflation from these scenarios with next-generation CMB experiments.