Perturbative region on non-Gaussian parameter space in single-field inflation

TL;DR

This paper calculates one-loop quantum corrections to curvature perturbations in single-field inflation, revealing bounds on non-Gaussianity and potential limitations of perturbation theory based on the size of these corrections.

Contribution

It provides a detailed analysis of one-loop corrections in single-field inflation and establishes bounds on primordial non-Gaussianity considering observed spectral tilt.

Findings

One-loop corrections are finite and inversely proportional to spectral tilt.

The observationally allowed non-Gaussianity region is within the perturbative regime.

Large one-loop corrections could indicate breakdown of perturbation theory.

Abstract

We calculate one-loop correction to the two-point functions of curvature perturbation in single-field inflation generated by cubic self-interaction. Incorporating the observed red-tilted spectrum of curvature perturbation, the relevant one-loop correction takes a finite value and inversely proportional to the spectral tilt. Requiring one-loop correction to be much smaller than the tree-level contribution leads to an upper bound on primordial non-Gaussianity. While observationally allowed region of non-Gaussian parameter space is found to be entirely included by the region, where one-loop correction is smaller than the tree-level contribution, an appreciably large region has one-loop correction larger than 1% or even 10% of the latter. If future observations conclude non-Gaussianity falls in such a region, then it would be important to incorporate higher-order corrections to the spectrum in order to achieve precise cosmology. In some extreme cases, where one-loop correction has a comparable magnitude to the tree-level contribution, it might indicate breakdown of the cosmological perturbation theory in the context of single-field inflation.