Vanishing of local non-Gaussianity in canonical single field inflation

TL;DR

This paper demonstrates that the observable local non-Gaussianity parameter $f_{NL}^{obs}$ vanishes during inflation in both attractor and non-attractor regimes when using Conformal Fermi Coordinates, indicating no detectable local non-Gaussianity.

Contribution

It introduces a gauge-invariant method using Conformal Fermi Coordinates to show the vanishing of observable local non-Gaussianity in all single field inflation models.

Findings

Observable $f_{NL}^{obs}$ is zero during inflation in both regimes.

The squeezed limit of the 3-point function vanishes in CFC frame.

Cancellation of non-Gaussianity persists after inflation.

Abstract

We study the production of observable primordial local non-Gaussianity in two opposite regimes of canonical single field inflation: attractor (standard single field slow-roll inflation) and non attractor (ultra slow-roll inflation). In the attractor regime, the standard derivation of the bispectrum's squeezed limit using co-moving coordinates gives the well known Maldacena's consistency relation $f_{NL} = 5(1-n_{s})/12$. On the other hand, in the non-attractor regime, the squeezed limit offers a substantial violation of this relation given by $f_{NL} = 5/2$. In this work we argue that, independently of whether inflation is attractor or non-attractor, the size of the observable primordial local non-Gaussianity is predicted to be $f_{NL}^{obs} = 0$ (a result that was already understood to hold in the case of attractor models). To show this, we follow the use of the so-called Conformal Fermi Coordinates (CFC), recently introduced in the literature. These coordinates parametrize the local environment of inertial observers in a perturbed FRW spacetime, allowing one to identify and compute gauge invariant quantities, such as $n$-point correlation functions. Concretely, we find that during inflation, after all the modes have exited the horizon, the squeezed limit of the 3-point correlation function of curvature perturbations vanishes in the CFC frame, regardless of the inflationary regime. We argue that such a cancellation should persist after inflation ends.