Curvature dependence of quantum gravity with scalars

TL;DR

This paper investigates how curvature influences quantum gravity coupled to scalars by computing curvature-dependent correlation functions, extending previous work to negative curvatures, and analyzing stability and solutions of the quantum equations of motion.

Contribution

It extends the analysis of curvature-dependent quantum gravity to include negative curvatures and scalar couplings, providing new insights into solution stability and the curvature potential.

Findings

Quantum equations of motion have two solutions for all scalar field numbers.

Negative curvature solution is a minimum, positive curvature solution is a maximum.

Large positive curvature solutions may be stable for all scalar flavors.

Abstract

We compute curvature-dependent graviton correlation functions and couplings as well as the full curvature potential $f(R)$ in asymptotically safe quantum gravity coupled to scalars. The setup is based on a systematic vertex expansion about metric backgrounds with constant curvatures initiated in arXiv:1711.09259 for positive curvatures. We extend these results to negative curvature and investigate the influence of minimally coupled scalars. The quantum equation of motion has two solutions for all accessible numbers of scalar fields. We observe that the solution at negative curvature is a minimum, while the solution at positive curvature is a maximum. We find indications that the solution to the equation of motions for scalar-gravity systems is at large positive curvature, for which the system might be stable for all scalar flavours.