We study the details of preheating in Palatini Higgs inflation. We show, that contrary to what happens in the metric formulation of the model, the Universe does not reheat through the creation of gauge bosons only, but also through the tachyonic production of Higgs excitations. The latest entropy production channel turns out to be very efficient and leads to an almost instantaneous onset of radiation domination after the end of inflation. As compared to the metric case, this reduces the number of e-folds needed to solve the usual hot big bang problems while leading to a smaller spectral index for the primordial spectrum of density perturbations.

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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 tensorto-scalar ratio is r ≤ 1.2 × 10 −3 in the metric case and r ≤ 2.2 × 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 treelevel plateau or at the critical point, making it possible to distinguish hilltop inflation from these scenarios with next-generation CMB experiments.

We study the production of primordial black hole (PBH) dark matter in the case when the Standard Model Higgs coupled non-minimally to gravity is the inflaton. PBHs can be produced if the Higgs potential has a near-critical point due to quantum corrections. In this case the slow-roll approximation may be broken, so we calculate the power spectrum numerically. We consider both the metric and the Palatini formulation of general relativity. Combining observational constraints on PBHs and on the CMB spectrum we find that PBHs can constitute all of the dark matter only if they evaporate early and leave behind Planck mass relics. This requires the potential to have a shallow local minimum, not just a critical point. The initial PBH mass is then below 10 6 g, and predictions for the CMB observables are the same as in tree-level Higgs inflation, n s = 0.96 and r = 5 × 10 −3 (metric) or r = 4 × 10 −8 . . . 2 × 10 −7 (Palatini).