Scaling behavior of quantum four-geometries

TL;DR

This paper proposes a new conformal invariant phase of quantum gravity at large scales, derived from quantum fluctuations of the conformal factor, with specific scaling relations and predictions testable via numerical simulations.

Contribution

It introduces a scale invariant phase of quantum gravity driven by conformal fluctuations and derives testable scaling relations for observables in this phase.

Findings

Evidence of a conformal invariant phase from numerical results

Predicted form of the critical curve in coupling space

Scaling of Newtonian coupling with volume for continuum limit

Abstract

We propose that large quantum fluctuations of the conformal factor drastically modify classical general relativity at cosmological distance scales, resulting in a scale invariant phase of quantum gravity in the far infrared. We derive scaling relations for the partition function and physical observables in this conformal phase, and suggest quantitative tests of these relations in numerical simulations of simplicial four geometries with $S^4$ topology. In particular, we predict the form of the critical curve in the coupling constant plane, and determine the scaling of the Newtonian coupling with volume which permits a sensible continuum limit. The existing numerical results already provide some evidence of this new conformal invariant phase of quantum gravity.