Asymptotic Safety of Gravity Coupled to Matter

TL;DR

This paper proves the stability of the asymptotic safety fixed point in gravity when coupled to scalar matter, showing that the fixed point persists under various matter configurations and can address triviality issues.

Contribution

It demonstrates the stability of the asymptotic safety fixed point in gravity with scalar matter and explores how matter content affects the fixed point and triviality solutions.

Findings

Stable fixed point persists with scalar matter

Critical surface is four-dimensional

Existence of asymptotically free scalar potentials for some matter types

Abstract

Nonperturbative treatments of the UV limit of pure gravity suggest that it admits a stable fixed point with positive Newton's constant and cosmological constant. We prove that this result is stable under the addition of a scalar field with a generic potential and nonminimal couplings to the scalar curvature. There is a fixed point where the mass and all nonminimal scalar interactions vanish while the gravitational couplings have values which are almost identical to the pure gravity case. We discuss the linearized flow around this fixed point and find that the critical surface is four-dimensional. In the presence of other, arbitrary, massless minimally coupled matter fields, the existence of the fixed point, the sign of the cosmological constant and the dimension of the critical surface depend on the type and number of fields. In particular, for some matter content, there exist polynomial asymptotically free scalar potentials, thus providing a solution to the well-known problem of triviality.