Cancellation of one-loop correction to soft tensor power spectrum

TL;DR

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

Contribution

It derives a soft tensor effective field theory showing the non-existence of scale-invariant one-loop corrections from small-scale scalar perturbations.

Findings

No scale-invariant one-loop corrections to tensor spectra from small-scale scalar fluctuations.

The result is rooted in the diffeomorphism invariance of general relativity.

Loop calculations in the soft limit confirm the absence of corrections.

Abstract

We demonstrate that there are no scale-invariant one-loop corrections to the superhorizon tensor perturbations from small-scale (potentially enhanced) scalar perturbations, irrespective of the details of inflationary background time evolution. For this purpose we derive a soft tensor effective field theory at leading order in the gradient expansion by integrating out small-scale scalar fluctuations in a general time-dependent background over the Schwinger-Keldysh contour, i.e., we perform loop calculations in the soft limit of external momentum. The absence of scale-invariant corrections originates from the diffeomorphism invariance of general relativity and is therefore unavoidable.