Near-Critical Higgs Inflation in Metric and Metric-Affine Schemes of Gravity*

Higgs inflation proposes the Standard Model Higgs field as the inflaton for early-universe cosmic inflation. Critical Higgs inflation introduces loop-corrections to the potential at high energies, which near the perturbative inflection point may drive slow-roll inflation that matches cosmological observables such as the power spectrum of the anisotropies in the cosmic microwave background (CMB). Recent unitarity calculations find that the cut-off scale for self-consistent Higgs inflation in the metric gravity formulation falls well below the expectation value of the inflaton condensate. The metric-affine (Palatini) formulation of gravity yields a higher cutoff, but to yield a close match to CMB observations it typically requires unrealistic running of the Standard Model couplings. Here, we investigate the prospects for self-consistent Higgs inflation driven by a loop-corrected Higgs potential in both the metric and Palatini schemes by 1) analytically deriving and comparing the slow-roll parameters for metric and Palatini gravity at the tree and loop-corrected level, 2) numerically solving for the background field evolution and corresponding observables during inflation, as well as comparing the relevant scales during inflation with the unitarity scale, and 3) measuring deviations from best-fit values for the Standard Model couplings required to match CMB observations while respecting unitarity. Finally, we consider the possibility that while the Higgs field is undergoing slow-roll inflation near criticality it forms primordial black holes (PBHs). We calculate the peak in the power spectrum of the scalar curvature perturbations and the frequency at which their gravitational wave (GW) signal peaks, and investigate the prospects for detecting PBH formation with next-generation GW detectors.