Numerical 1-loop correction from a potential yielding ultra-slow-roll dynamics

TL;DR

This paper reevaluates the one-loop correction to the scalar power spectrum in single-field inflation models with ultra-slow-roll phases, finding that the correction remains significant even with smooth transitions, impacting small-scale phenomenology.

Contribution

It provides a numerical analysis of 1-loop corrections considering smooth transitions, confirming their non-negligible impact on large-scale spectrum in realistic inflation models.

Findings

1-loop correction is a few percent of the tree-level spectrum for relevant small-scale peaks.

Smooth transitions do not significantly reduce the 1-loop correction.

The correction remains substantial for models with primordial black hole production potential.

Abstract

Single-field models of inflation might lead to amplified scalar fluctuations on small scales due, for example, to a transient ultra-slow-roll phase. It was argued by Kristiano $\&$ Yokoyama in arXiv:2211.03395 that the enhanced amplitude of the scalar power spectrum on small scales has the potential to induce a sizeable 1-loop correction to the spectrum at large scales. In this work, we repeat the calculation for the 1-loop correction presented in arXiv:2211.03395. We closely follow their assumptions but evaluate the loop numerically. This allows us to consider both instantaneous and smooth transitions between the slow-roll and ultra-slow-roll phases. In particular, we generate models featuring realistic, smooth evolution from an analytic inflationary potential. We find that, upon fixing the amplitude of the peak in the power spectrum at short scales, the resulting 1-loop correction is not significantly reduced by considering a smooth evolution. In particular, for a power spectrum with a tree-level peak amplitude potentially relevant for small-scale phenomenology, e.g. primordial black hole production, the 1-loop correction on large scales is a few percent of the tree-level power spectrum.