Leading Logarithm Quantum Gravity

TL;DR

This paper develops a new stochastic technique to sum leading secular effects in quantum gravity during inflation, addressing perturbation theory breakdown caused by long-wavelength gravitons.

Contribution

It generalizes a method combining stochastic formalism and renormalization group to quantum gravity, enabling analysis of secular growth in gravitational phenomena.

Findings

Derived a Langevin equation for quantum gravity during inflation

Demonstrated the technique's potential to sum secular effects in graviton loops

Provides a new tool for understanding long-term quantum gravitational dynamics

Abstract

The continual production of long wavelength gravitons during primordial inflation endows graviton loop corrections with secular growth factors. During a prolonged period of inflation these factors eventually overwhelm the small loop-counting parameter of $G H^2$, causing perturbation theory to break down. A technique was recently developed for summing the leading secular effects at each order in non-linear sigma models, which possess the same kind of derivative interactions as gravity. This technique combines a variant of Starobinsky's stochastic formalism with a variant of the renormalization group. We generalize the new technique to quantum gravity, resulting in a Langevin equation in which secular changes in gravitational phenomena are driven by stochastic fluctuations of the graviton field.