Cancellation of loop corrections to soft scalar power spectrum

TL;DR

This paper proves that one-loop quantum corrections do not alter the scale-invariance of the superhorizon curvature perturbations during inflation, due to underlying symmetry principles.

Contribution

It demonstrates the absence of one-loop scale-invariant corrections in a general inflationary context, including ultra-slow-roll scenarios, using symmetry analysis and explicit calculations.

Findings

One-loop corrections do not affect superhorizon curvature perturbations.

Dilatation symmetry ensures cancellation of scale-invariant corrections.

Results hold even with enhanced small-scale scalar perturbations.

Abstract

We prove the absence of scale-invariant one-loop corrections to the superhorizon curvature perturbations from small-scale (potentially enhanced) scalar perturbations in a general inflationary setup, including the transient ultra-slow-roll scenario. We demonstrate this by analyzing the symmetry structure of an in-in effective field theory for the soft curvature perturbations, and by explicitly performing one-loop calculations, integrating out hard modes in the soft limit of external momenta. The dilatation symmetry, respected by a counter term necessary for the tadpole cancellation, guarantees the cancellation of scale-invariant corrections.