Absence of one-loop effects on large scales from small scales in non-slow-roll dynamics

TL;DR

This paper investigates whether small-scale modes can produce significant one-loop corrections to large-scale power spectra in non-slow-roll inflation, finding cancellations that negate such effects.

Contribution

It demonstrates that boundary terms and seemingly irrelevant interactions do not lead to non-suppressed one-loop corrections in non-slow-roll scenarios.

Findings

One-loop corrections from small scales are canceled by boundary terms.

Non-slow-roll dynamics do not produce volume-suppressed one-loop effects.

Boundary terms play a crucial role in the cancellation of potential corrections.

Abstract

We question the existence of one-loop corrections to the large-scale power spectrum from small-scale modes in non-slow-roll dynamics which are not volume suppressed by the ratio of the short to long distance scales. One-loop contributions proportional to the long wavelength tree-level power spectrum, and not sharing this suppression, have appeared in studies involving interactions singled out by the non-slow-roll dynamics. In this context, we show the relevance of seemingly irrelevant interactions terms, such as the one provided by total derivative terms (boundary terms), and how they equally lead to non-volume suppressed contributions and exact cancellations.