IR divergence does not affect the gauge-invariant curvature perturbation

TL;DR

This paper demonstrates that infrared divergences in loop corrections during inflation are gauge artifacts and do not affect gauge-invariant curvature perturbations, confirming their physical robustness.

Contribution

The authors explicitly construct gauge-invariant quantities and show that IR divergences are absent at leading order, clarifying the role of gauge choices and initial vacuum states.

Findings

IR divergence is a gauge artifact in single-field inflation

Gauge-invariant curvature perturbations are free from IR divergence at leading order

Subtle issues exist in specifying the initial vacuum state for gauge invariance

Abstract

We address the infrared(IR) divergence problem during inflation that appears in the loop corrections to the primordial perturbations. In our previous paper, we claimed that, at least in single field models, the IR divergence is originating from the gauge artifact. Namely, diverging IR corrections should not appear in genuine gauge-invariant observables. We propose here one simple but explicit example of such gauge-invariant quantities. Then, we explicitly calculate such a quantity to find that the IR divergence is absent at the leading order in the slow-roll approximation for the usual scale invariant vacuum state. At the same time we notice that there is a subtle issue on the gauge-invariance in how to specify the initial vacuum state.