# Invariant Measure of the One Loop Quantum Gravitational Back-Reaction on Inflation

## TL;DR

This paper calculates the one-loop quantum gravitational back-reaction on inflation using dimensional regularization, showing that the correction can be renormalized with local counterterms, supporting the idea that secular effects are two-loop phenomena.

## Contribution

It demonstrates the renormalization of a nonlocal invariant operator in quantum gravity on de Sitter space at one loop, aligning with predictions about secular back-reaction.

## Key findings

- One-loop correction is fully absorbed by local counterterms.
- Secular back-reaction effects are predicted to appear at two-loop order.
- Renormalization approach simplifies understanding quantum effects during inflation.

## Abstract

We use dimensional regularization in pure quantum gravity on de Sitter background to evaluate the one loop expectation value of an invariant operator which gives the local expansion rate. We show that the renormalization of this nonlocal composite operator can be accomplished using the counterterms of a simple local theory of gravity plus matter, at least at one loop order. This renormalization completely absorbs the one loop correction, which accords with the prediction that the lowest secular back-reaction should be a 2-loop effect.