Infrared divergences for free quantum fields in cosmological spacetimes

Abstract

We investigate the nature of infrared divergences for the free graviton and inflaton two-point functions in flat Friedman–Lemaître–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 , where p is the momentum, in the infrared, then it can be made to behave like 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 to . 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.