A Simplified Quantum Gravitational Model of Inflation

TL;DR

This paper presents a simplified quantum gravity model of inflation using the leading logarithm approximation, focusing on the cosmological constant's renormalization and quantum back-reaction effects, with implications for primordial perturbations.

Contribution

It introduces a novel simplified model of quantum gravity during inflation, emphasizing the leading logarithm approximation and operator dynamics, and explores quantum back-reaction effects.

Findings

The model's dynamical assumption captures correct time dependence.

It can produce primordial perturbations of appropriate strength.

Provides a partial test of the null hypothesis regarding infrared gravitons.

Abstract

Inflationary quantum gravity simplifies drastically in the leading logarithm approximation. We show that the only counterterm which contributes in this limit is the 1-loop renormalization of the cosmological constant. We go further to make a simplifying assumption about the operator dynamics at leading logarithm order. This assumption is explicitly implemented at 1- and 2-loop orders, and we describe how it can be implemented nonperturbatively. We also compute the expectation value of an invariant observable designed to quantify the quantum gravitational back-reaction on inflation. Although our dynamical assumption may not prove to be completely correct, it does have the right time dependence, it can naturally produce primordial perturbations of the right strength, and it illustrates how a rigorous application of the leading logarithm approximation might work in quantum gravity. It also serves as a partial test of the "null hypothesis" that there are no significant effects from infrared gravitons.