A generalized non-Gaussian consistency relation for single field
  inflation
  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.
