Generation and characterization of large non-Gaussianities in single field inflation

Abstract

Inflation driven by a single, minimally coupled, slowly rolling field generically yields a negligible primordial non-Gaussianity. We discuss two distinct mechanisms by which a non-trivial potential can generate large non-Gaussianities. Firstly, if the inflaton traverses a feature in the potential, or if the inflationary phase is short enough so that initial transient contributions to the background dynamics have not been erased, modes near horizon crossing can acquire significant non-Gaussianities. Secondly, potentials with small-scale structure may induce significant non-Gaussianities while the relevant modes are deep inside the horizon. The first case includes the ‘step’ potential we previously analyzed while the second ‘resonance’ case is novel. We derive analytic approximations for the three-point terms generated by both mechanisms written as products of functions of the three individual momenta, permitting the use of efficient analysis algorithms. Finally, we present a significantly improved approach to regularizing and numerically evaluating the integrals that contribute to the three-point function.