Unifying attractor and non-attractor models of inflation under a single soft theorem

Abstract

We study the generation of local non-Gaussianity in models of canonical single field inflation when their backgrounds are either attractor or non-attractor. We show that the invariance of inflation under space-time diffeomorphisms can be exploited to make powerful statements about the squeezed limit of the primordial bispectrum of curvature perturbations, valid to all orders in slow roll parameters. In particular, by neglecting departures from the adiabatic evolution of long-wavelength modes (for instance, produced in sharp transitions between slow-roll and ultra slow-roll phases), we derive a general expression for the bispectrum's squeezed limit in co-moving coordinates. This result consists in the standard Maldacena's consistency relation (proportional to the spectral index of the power spectrum) plus additional terms containing time derivatives of the power spectrum. In addition, we show that it is always possible to write the perturbed metric in conformal Fermi coordinates, independently of whether the inflationary background is attractor or non-attractor, allowing the computation of the physical primordial bispectrum's squeezed limit as observed by local inertial observers. We find that in the absence of sudden transitions between attractor and non-attractor regimes, observable local non-Gaussianity is generically suppressed. Our results imply that large local non-Gaussianity is not a generic consequence of non-attractor backgrounds.