Strong restriction on inflationary vacua from the local gauge invariance III: Infrared regularity of graviton loops

Abstract

It has been claimed that the super-Hubble modes of the graviton generated during inflation can make loop corrections diverge. Even if we introduce an infrared (IR) cutoff at a comoving scale as an ad hoc but practical method of regularization, we encounter secular growth, which may lead to the breakdown of perturbative expansion for a sufficiently long-lasting inflation. In this paper, we show that the IR pathology concerning the graviton can be attributed to the presence of residual gauge degrees of freedom in the local observable universe, as in the case of the adiabatic curvature perturbation. We will show that choosing the Euclidean vacuum as the initial state ensures invariance under the above-mentioned residual gauge transformations. We will also show that, as long as we consider a gauge invariant quantity in the local universe, we encounter neither IR divergence nor secular growth. The argument in this paper applies to general single-field models of inflation up to a sufficiently high order in perturbation.