A generalized non-Gaussian consistency relation for single field inflation

TL;DR

This paper derives a generalized non-Gaussian consistency relation for single-field inflation, linking the squeezed limit of the bispectrum to spacetime symmetries, applicable even when curvature perturbations do not freeze.

Contribution

It introduces a new invariance-based approach to derive the squeezed limit of the bispectrum, extending Maldacena's relation to broader inflationary scenarios.

Findings

Derivation of a generalized consistency relation using spacetime diffeomorphisms

Application to ultra slow-roll inflation showing violation of standard relation

Insight into how long-wavelength modes modulate shorter wavelengths

Abstract

We show that a perturbed inflationary spacetime, driven by a canonical single scalar field, is invariant under a special class of coordinate transformations together with a field reparametrization of the curvature perturbation in co-moving gauge. This transformation may be used to derive the squeezed limit of the 3-point correlation function of the co-moving curvature perturbations valid in the case that these do not freeze after horizon crossing. This leads to a generalized version of Maldacena's non-Gaussian consistency relation in the sense that the bispectrum squeezed limit is completely determined by spacetime diffeomorphisms. Just as in the case of the standard consistency relation, this result may be understood as the consequence of how long-wavelength modes modulate those of shorter wavelengths. This relation allows one to derive the well known violation to the consistency relation encountered in ultra slow-roll, where curvature perturbations grow exponentially after horizon crossing.