Infrared Propagator Corrections for Constant Deceleration

TL;DR

This paper derives the scalar propagator in a D-dimensional universe with constant deceleration, addressing infrared divergences and computing the stress-energy tensor expectation value.

Contribution

It provides a new derivation of the propagator using operator formalism for arbitrary constant deceleration, including infrared correction treatment.

Findings

Infrared divergences are properly handled with finite spatial sections.

The propagator is explicitly constructed for arbitrary deceleration.

The scalar stress-energy tensor expectation value is computed.

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.