Infrared divergences for free quantum fields in cosmological spacetimes

TL;DR

This paper demonstrates that infrared divergences in free graviton and inflaton two-point functions in cosmological spacetimes can be mitigated using large gauge transformations, making these functions finite for many inflationary models.

Contribution

It shows that large gauge transformations can increase the infrared power of two-point functions by four, resolving divergences in a broad class of inflationary scenarios.

Findings

Infrared divergences can be removed by large gauge transformations.

Two-point functions can be made finite for many inflationary potentials.

Gauge-invariant smearing increases the infrared power by four.

Abstract

We investigate the nature of infrared divergences for the free graviton and inflaton two-point functions in flat Friedman-Lema\^{\i}tre-Robertson-Walker spacetime. These divergences arise because the momentum integral for these two-point functions diverges in the infrared. It is straightforward to see that the power of the momentum in the integrand can be increased by $2$ in the infrared using large gauge transformations, which are sufficient for rendering these two-point functions infrared finite for slow-roll inflation. In other words, if the integrand of the momentum integral for these two-point functions behaves like $p^{-2\nu}$, where $p$ is the momentum, in the infrared, then it can be made to behave like $p^{-2\nu+2}$ by large gauge transformations. On the other hand, it is known that, if one smears these two-point functions in a gauge-invariant manner, the power of the momentum in the integrand is changed from $p^{-2\nu}$ to $p^{-2\nu+4}$. This fact suggests that the power of the momentum in the integrand for these two-point functions can be increased by $4$ using large gauge transformations. In this paper we show that this is indeed the case. Thus, the two-point functions for the graviton and inflaton fields can be made finite by large gauge transformations for a large class of potentials and states in single-field inflation.