On the Validity of the Effective Theory of (Multi-)Field Inflation

Abstract

Motivated by trans-Planckian issues in inflation, we determine the Hilbert space and amplitudes of quantum perturbations in the general low-energy effective theory of (multi-)field inflation without relying on the sub-horizon limit. The scalar sector is the most intricate, featuring field mixings and second-class constraints, which we handle using Dirac brackets. These results enable us to estimate the magnitude of higher-derivative corrections. In the specific case of slow-roll inflation, such estimate can be expressed in terms of the first slow-roll parameter $ε$ for a given cutoff $Λ$. We apply our results to several inflationary models with finite $Λ$: Higgs inflation, the Starobinsky model, natural inflation and hilltop inflation.