Natural selection of inflationary vacuum required by infra-red regularity and gauge-invariance

TL;DR

The paper tackles whether inflationary IR divergences are physical or gauge artifacts in single-field inflation. It constructs a genuine gauge-invariant curvature observable $^gR$ via geodesic-normal coordinates and analyzes its one-loop IR behavior up to ${\cal O}(\varepsilon^2)$, including gravitons, showing that potentially divergent terms cancel when the initial state respects residual gauge symmetries. A gauge-invariant initial vacuum is derived through conditions on mode functions, ensuring IR regularity and compatibility with canonical quantization; the graviton loops are shown not to introduce IR divergences in these observables. The work clarifies how boundary conditions and the choice of initial state affect the consistency of inflationary perturbation theory and provides a framework for extending IR regularity results to higher orders.

Abstract

It has been an issue of debate whether the inflationary infrared(IR) divergences are physical or not. Our claim is that, at least, in single-field models, the answer is "No," and that the spurious IR divergence is originating from the careless treatment of the gauge modes. In our previous work we have explicitly shown that the IR divergence is absent in the genuine gauge-invariant quantity at the leading order in the slow-roll approximation. We extend our argument to include higher-order slow-roll corrections and the contributions from the gravitational waves. The key issue is to assure the gauge invariance in the choice of the initial vacuum, which is a new concept that has not been considered in conventional calculations.