Scalar Contribution to the Graviton Self-Energy during Inflation

TL;DR

This paper calculates the one-loop quantum correction to the graviton self-energy caused by a massless scalar during inflation, providing a tool to study quantum effects on gravitational wave propagation.

Contribution

It presents a detailed computation of the scalar contribution to the graviton self-energy during inflation, including renormalization and a form suitable for quantum corrections.

Findings

Agreement with previous stress tensor correlator results

Renormalized self-energy expressed as transverse differential operators

Framework for studying quantum effects on graviton propagation during inflation

Abstract

We use dimensional regularization to evaluate the one loop contribution to the graviton self-energy from a massless, minimally coupled scalar on a locally de Sitter background. For noncoincident points our result agrees with the stress tensor correlators obtained recently by Perez-Nadal, Roura and Verdaguer. We absorb the ultraviolet divergences using the $R^2$ and $C^2$ counterterms first derived by 't Hooft and Veltman, and we take the $D=4$ limit of the finite remainder. The renormalized result is expressed as the sum of two transverse, 4th order differential operators acting on nonlocal, de Sitter invariant structure functions. In this form it can be used to quantum-correct the linearized Einstein equations so that one can study how the inflationary production of infrared scalars affects the propagation of dynamical gravitons and the force of gravity.