Predictions for non-Gaussianity from non-local inflation

In our previous work the non-linearity parameter fNL, which characterizes non-Gaussianity in the cosmic microwave background, was estimated for a class of inflationary models based on non-local field theory. These models include p-adic inflation and generically have the remarkable property that slow roll inflation can proceed even with an extremely steep potential. Previous calculations found that large non-Gaussianity is possible; however, the technical complications associated with studying perturbations in theories with infinitely many derivatives forced us to provide only an order of magnitude estimate for fNL. We reconsider the problem of computing fNL in non-local inflation models, showing that a particular choice of field basis and recent progress in cosmological perturbation theory makes an exact computation possible. We provide the first quantitatively accurate computation of the bispectrum in non-local inflation, confirming our previous claim that it can be observably large. We show that the shape of the bispectrum in this class of models makes it observationally distinguishable from Dirac-Born-Infeld inflation models.