Predictions for Nongaussianity from Nonlocal Inflation

TL;DR

The paper addresses how nonlocal inflation models generate primordial non-Gaussianity, focusing on the bispectrum and the nonlinearity parameter $f_{NL}$. By reformulating the theory with a dressed, canonical field and applying modern perturbation techniques, it computes the bispectrum exactly, revealing that the nonlocal cubic coupling can yield a large equilateral $f_{NL}$ with a shape distinct from DBI inflation. In particular, $p$-adic inflation can produce observable $f_{NL}$ for natural choices of the string coupling, with $f_{NL}$ scaling roughly as $\sqrt{p}/\ln p$ for large $p$, and thus potentially compatible with current hints of non-Gaussianity. The results emphasize the need for UV-complete nonlocal dynamics to avoid ghosts and suggest that future observations of the primordial bispectrum could probe physics at the quantum gravity scale.

Abstract

In our previous work the nonlinearity parameter f_NL, which characterizes nongaussianity in the cosmic microwave background, was estimated for a class of inflationary models based on nonlocal 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 nongaussianity 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 f_NL. We reconsider the problem of computing f_NL in nonlocal 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 nonlocal 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.