Coincident Massless, Minimally Coupled Scalar Correlators on General Cosmological Backgrounds

TL;DR

This paper derives analytic approximations for scalar propagator correlators and their derivatives in inflationary cosmological backgrounds, aiding in summing leading logarithms from inflationary graviton loops.

Contribution

It provides new analytic approximations for scalar correlators on general inflationary backgrounds using dimensional regularization.

Findings

Derived expressions for scalar propagator coincidence limits and derivatives

Applicable to general inflationary cosmological geometries

Facilitates summing leading logarithms in inflationary loop calculations

Abstract

The coincidence limits of the massless, minimally coupled scalar propagator and its first two derivatives have great relevance for the project of summing up the leading logarithms induced by loops of inflationary gravitons. We use dimensional regularization to derive good analytic approximations for the three quantities on a general cosmological background geometry which underwent inflation.