Curvature dependence of quantum gravity

TL;DR

This paper explores how quantum gravity's behavior depends on curvature by analyzing fixed points and potentials on curved backgrounds, providing new insights into the phase diagram and matter interactions.

Contribution

It introduces curvature-dependent UV fixed point functions and solves quantum and background equations of motion with matter, advancing understanding of quantum gravity on curved spaces.

Findings

Curvature-dependent UV fixed point functions obtained.

Solutions to quantum and background equations computed with matter.

Results are robust against truncation changes.

Abstract

We investigate the phase diagram of quantum gravity with a vertex expansion about constantly-curved backgrounds. The graviton two- and three-point function are evaluated with a spectral sum on a sphere. We obtain, for the first time, curvature-dependent UV fixed point functions of the dynamical fluctuation couplings $g^*(R)$, $\mu^*(R)$, and $\lambda_3^*(R)$, and the background $f(R)$-potential. Based on these fixed point functions we compute solutions to the quantum and the background equation of motion with and without Standard Model matter. We have checked that the solutions are robust against changes of the truncation.