Infrared Propagator Corrections for Constant Deceleration

TL;DR

This work resolves infrared pathologies in the massless, minimally coupled scalar propagator on a $D$-dimensional FLRW background with constant $\epsilon$ by replacing the infinite-space mode sum with a finite-space (torus) formulation, then adding homogeneous solutions to cancel IR divergences. The authors derive the corrected propagator, compute the one-loop scalar stress-energy tensor, and show that all infrared singularities cancel when the finite-space corrections are included, leaving finite, physically meaningful results that exhibit logarithmic dependence on the scale factor in certain regimes. They renormalize UV divergences via an $R^2$ counterterm and provide explicit expressions for the finite parts, including special treatment of poles from digamma functions. The results clarify the proper handling of infrared effects in cosmological quantum fields and underscore the importance of initial conditions and finite spatial extents for decelerating universes, with implications for backreaction and early-universe physics.

Abstract

We derive the propagator for a massless, minimally coupled scalar on a $D$-dimensional, spatially flat, homogeneous and isotropic background with arbitrary constant deceleration parameter. Our construction uses the operator formalism, by integrating the Fourier mode sum. We give special attention to infrared corrections from the nonzero lower limit associated with working on finite spatial sections. These corrections eliminate infrared divergences that would otherwise be incorrectly treated by dimensional regularization, resulting in off-coincidence divergences for those special values of the deceleration parameter at which the infrared divergence is logarithmic. As an application we compute the expectation value of the scalar stress-energy tensor.