How Gaussian can our Universe be?

TL;DR

This paper demonstrates that the minimal primordial non-Gaussianity in our universe is non-zero and scales with the tilt of the scalar spectral index, challenging the idea that it could be arbitrarily low.

Contribution

The authors explicitly show using Conformal Fermi Coordinates that a non-zero contribution to primordial non-Gaussianity always exists, proportional to the spectral tilt, contrary to previous suspicions.

Findings

Primordial non-Gaussianity has a lower bound proportional to the spectral tilt.

The minimal non-Gaussianity scales as $k_ ext{long}^2/k_ ext{short}^2$ in the squeezed limit.

The amplitude of this non-Gaussianity is approximately 0.1 times the spectral tilt deviation.

Abstract

Gravity is a non-linear theory, and hence, barring cancellations, the initial super-horizon perturbations produced by inflation must contain some minimum amount of mode coupling, or primordial non-Gaussianity. In single-field slow-roll models, where this lower bound is saturated, non-Gaussianity is controlled by two observables: the tensor-to-scalar ratio, which is uncertain by more than fifty orders of magnitude; and the scalar spectral index, or tilt, which is relatively well measured. It is well known that to leading and next-to-leading order in derivatives, the contributions proportional to the tilt disappear from any local observable, and suspicion has been raised that this might happen to all orders, allowing for an arbitrarily low amount of primordial non-Gaussianity. Employing Conformal Fermi Coordinates, we show explicitly that this is not the case. Instead, a contribution of order the tilt appears in local observables. In summary, the floor of physical primordial non-Gaussianity in our Universe has a squeezed-limit scaling of $k_\ell^2/k_s^2$, similar to equilateral and orthogonal shapes, and a dimensionless amplitude of order $0.1\times(n_\mathrm{s}-1)$.