Constructing Infrared Finite Propagators in Inflating Space-time

TL;DR

Massless fields in de Sitter-like spacetimes exhibit infrared divergences in standard Feynman propagators, complicating loop predictions in inflation. The authors introduce zero-mode modification, a boundary-condition adjustment for the zero-frequency mode, and a comoving infrared scale $k_{IR}$ to render propagators IR finite without removing the massless nature. They provide explicit construction for the scalar propagator $G^{fin}_F$ via an IR cutoff $r$ and a compensating term $f(k_{IR}/r)$, with a parallel treatment for the two-point function; they also extend the method to gravitons by choosing a gauge that fixes zero-mode shifts, yielding finite gauge-invariant observables. The approach offers a practical alternative to hard IR cutoffs and clarifies how an observationally determined $k_{IR}$ enters loop calculations in inflationary cosmology.

Abstract

The usual (Bunch-Davies) Feynman propagator of a massless field is not well defined in an expanding universe due to the presence of infrared divergences. We propose a new propagator which yields infrared finite answers to any correlation function. The key point is that in a de Sitter spacetime there is an ambiguity in the zero-mode of the propagator. This ambiguity can be used to cancel the apparent divergences which arise in some loop calculations in eternally (or semi-eternally) inflating spacetime. We refer to this process as zero-mode modification. The residual ambiguity is fixed by observational measurement. We also discuss the application of this method to calculations involving the graviton propagator.