Field redefinitions, perturbative unitarity and Higgs inflation

Abstract

For inflation driven by the Higgs field coupled non-minimally to gravity, we study the cutoff energy scale above which perturbation theory breaks down. Employing the metric formulation, we first give an overview of known results and then provide a new way to calculate a lower bound on the cutoff. Our approach neither relies on a gauge choice nor does it require any calculation of amplitudes. Instead, it exploits the fact that the S-matrix is invariant under field redefinitions. In agreement with previous findings, we demonstrate that the cutoff is significantly higher during inflation than in vacuum, which ensures the robustness of semi-classical predictions. Along the way, we generalize our findings to the Palatini formulation and comment on a useful parametrization of the Higgs doublet in both scenarios.

Higgs-Dilaton inflation in Einstein-Cartan gravity

“…From the formal point of view, the two formulations display also a different range of validity. In particular, while the inflationary plateau is always of the order O(M P /ξ), the associated cut-off scales signaling the potential violation of tree-level unitarity are significantly different for fluctuations computed around the electroweak vacuum [28][29][30][31][32][33][34][35], Λ metric ∼ M P /ξ and Λ Palatini ∼ M P / √ ξ, being the Palatini one parametrically larger. This reduces the uncertainties associated to the non-renormalizability of the Standard Model non-minimally coupled to gravity and eases the connection between inflationary observables and collider experiments in Palatini Higgs inflation [25].…”