A generalized non-Gaussian consistency relation for single field inflation

Abstract

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