Resumming Photon Loops for Inflationary Gravity

TL;DR

This paper analyzes the 1-loop photon contribution to graviton self-energy in de Sitter space, showing no local conservation obstacle, and finds a secular growth in the Weyl tensor components that can be resummed via renormalization group methods.

Contribution

It demonstrates the absence of local conservation issues for photon loops and introduces a resummation approach for secular growth in inflationary gravity.

Findings

No local conservation obstacle for photon loops.

Secular growth in Weyl tensor components.

Resummation of secular effects using renormalization group.

Abstract

A previous calculation of the 1-loop photon contribution to the graviton self-energy on de Sitter background is considered. We first show that there is no local obstacle to conservation, unlike the contribution from a loop of massless, minimally coupled scalars. This is correlated to the absence of an Eddington ($R^2$) counterterm and to the vanishing of the stress tensor when the photon in integrated out in the presence of a constant graviton field. We also show that there is a secularly growing 1-loop contribution to the electric components of the Weyl tensor for plane wave gravitons. Its coefficient agrees with that of the secular 1-loop correction to the Newtonian potential, and both can be resummed using a variant of the renormalization group.