Precision Unitarity Calculations in Inflationary Models

We revisit perturbative unitarity in scalar field inflation with a nonminimal coupling, with Higgs inflation serving as the most prominent example. Although such models are phenomenologically successful, it is critical to examine whether or not unitarity violations spoil their theoretical self-consistency. The analysis of these issues has so far typically relied on order-of-magnitude estimates of scattering amplitudes, which are appropriate for generic parameters. It is not evident that these methods apply to scenarios relying on a near-critical inflationary potential, for which an interplay of both small scalar self-couplings and nonminimal couplings could partially alleviate the unitarity issues. To allow for an exploration of this possibility, we consider the full $S$-matrix for the relevant scattering processes, taking into account important phase space volume factors, leading to a precise evaluation of the cut-off scale. In the single-field case, we demonstrate that near-criticality raises the cut-off scale considerably, compared to previous estimates. In the multifield case, momentum-dependent self-interactions in the kinetic sector lower the cut-off compared to the single-field case to a value comparable to but slightly larger than previous estimates. We carefully study both the single-field and multifield cases in metric and metric-affine (Palatini) formulations of gravity, as well as introduce a new phenomenologically viable model with a canonical kinetic term and a significantly raised cut-off, and discuss the importance of background field effects.