Large Nongaussianity from Nonlocal Inflation

TL;DR

The paper demonstrates that single-field nonlocal hill-top inflation can yield large primordial nongaussianity, challenging the conventional expectation of small $f_{NL}$. By analyzing a general nonlocal action with an infinite-derivative kinetic operator and a hill-top potential, the authors derive the background dynamics, fluctuations, and a canonical curvature perturbation, and then compute the bispectrum to estimate $f_{NL}$. In the concrete case of $p$-adic inflation, they find $f_{NL}$ that can reach $\mathcal{O}(10^2)$ for plausible string couplings, with an explicit bound $p \lesssim 1.7\times 10^{13}$ yielding $f_{NL}\lesssim 120$, suggesting potential observability in future missions. They also illustrate that a toy model with an exponential kinetic function can produce similarly large $f_{NL}$, underscoring that nonlocal hill-top inflation generically accommodates sizeable non-Gaussian signatures. The work highlights the distinctive role of nonlocality in permitting large cubic couplings and slow-roll inflation on steep potentials, while acknowledging caveats such as neglect of metric perturbations and IR regulator effects, which require a more complete second-order perturbation analysis.

Abstract

We study the possibility of obtaining large nongaussian signatures in the Cosmic Microwave Background in a general class of single-field nonlocal hill-top inflation models. We estimate the nonlinearity parameter f_{NL} which characterizes nongaussianity in such models and show that large nongaussianity is possible. For the recently proposed p-adic inflation model we find that f_{NL} ~ 120 when the string coupling is order unity. We show that large nongaussianity is also possible in a toy model with an action similar to those which arise in string field theory.