A Bound Concerning Primordial Non-Gaussianity

TL;DR

The paper investigates whether second-order non-Gaussianities of light fields during inflation can meaningfully enhance the three-point function of the primordial curvature perturbation $ζ$. It employs the $δN$ formalism and Seery & Lidsey’s results for the field bispectrum to bound the extra contribution $Δf_{NL}$, then maximizes this bound under a fixed $ζ$ to relate it to slow-roll parameters via $r$ and $ε$. The main result is an upper bound $\frac{6}{5}|Δf_{NL}|_{\max}=\frac{11}{24}\sqrt{r\epsilon}$, which, given observational limits, yields $|Δf_{NL}|_{\max} \lesssim 0.04$, meaning the non-Gaussian contribution is too small to be observable. Consequently, the three-point correlator of $ζ$ can be accurately computed from the Gaussian part, aligning with Maldacena’s conclusions for single- and multi-field slow-roll scenarios.

Abstract

Seery and Lidsey have calculated the three-point correlator of the light scalar fields, a few Hubble times after horizon exit during inflation. Lyth and Rodriguez have calculated the contribution of this correlator to the three-point correlator of the primordial curvature perturbation. We calculate an upper bound on that contribution, showing that it is too small ever to be observable.