Superhorizon Curvature Perturbations Are Protected against One-Loop Corrections

TL;DR

This paper investigates the stability of superhorizon curvature perturbations during inflation, demonstrating they are protected against one-loop corrections even with small-scale enhancement during transitional periods.

Contribution

It provides a detailed analysis showing superhorizon curvature perturbations remain conserved at one-loop level despite small-scale amplification during slow-roll transitions.

Findings

Superhorizon perturbations are conserved at one-loop level during slow-roll periods.

Small-scale enhancements do not affect superhorizon perturbations at one-loop order.

The results hold even with ultra-slow-roll or resonant amplification periods.

Abstract

We examine one-loop corrections from small-scale curvature perturbations to the superhorizon-limit ones in single-field inflation models, which have recently caused controversy. We consider the case where the Universe experiences transitions of slow-roll (SR) $\to$ intermediate period $\to$ SR. The intermediate period can be an ultra-slow-roll period or a resonant amplification period, either of which enhances small-scale curvature perturbations. We assume that the superhorizon curvature perturbations are conserved at least during each of the SR periods. Within this framework, we show that the superhorizon curvature perturbations during the first and the second SR periods coincide at one-loop level in the slow-roll limit.