Hartree Approximation to the One Loop Quantum Gravitational Correction to the Graviton Mode Function on de Sitter

TL;DR

This paper employs the Hartree approximation to analyze one loop quantum gravitational corrections to graviton mode functions during inflation on de Sitter space, revealing growth in certain tensor components over time.

Contribution

It introduces a Hartree approximation approach to compute one loop quantum gravitational effects on graviton modes in de Sitter space, providing new insights into their late-time behavior.

Findings

One loop correction scales as G H^2 ln(a)/a^2 at late times.

Corrections cause growth in electric components of the linearized Weyl tensor.

The approach approximates the influence of inflationary gravitons on a single graviton.

Abstract

We use the Hartree approximation to the Einstein equation on de Sitter background to solve for the one loop correction to the graviton mode function. This should give a reasonable approximation to how the ensemble of inflationary gravitons affects a single external graviton. At late times we find that the one loop correction to the plane wave mode function $u(\eta,k)$ goes like $G H^2 \ln(a)/a^2$, where $a$ is the inflationary scale factor. One consequence is that the one loop corrections to the "electric" components of the linearized Weyl tensor grow compared to the tree order result.