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 $n_s\leq0.96$ in both the metric and the Palatini
formulation, the upper bound coinciding with the tree-level result. The
tensor-to-scalar ratio is $r\leq1.2\times10^{-3}$ in the metric case and
$r\leq2.2\times10^{-9}$ 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.
