Gravitational Wilson Loop and Large Scale Curvature

TL;DR

This paper investigates the gravitational Wilson loop in quantum gravity, showing how it can be computed in the strong coupling limit to reveal large-scale curvature and suggesting a De Sitter-like ground state with a positive cosmological constant.

Contribution

It introduces a systematic method to compute the gravitational Wilson loop in lattice quantum gravity and links it to large-scale curvature, indicating a positive cosmological constant.

Findings

Large-scale curvature can be derived from the Wilson loop in strong coupling quantum gravity.

The quantum ground state is likely positively curved, similar to De Sitter space.

The gravitational correlation length correlates with observed large-scale curvature.

Abstract

In a quantum theory of gravity the gravitational Wilson loop, defined as a suitable quantum average of a parallel transport operator around a large near-planar loop, provides important information about the large-scale curvature properties of the geometry. Here we shows that such properties can be systematically computed in the strong coupling limit of lattice regularized quantum gravity, by performing a local average over rotations, using an assumed near-uniform measure in group space. We then relate the resulting quantum averages to an expected semi-classical form valid for macroscopic observers, which leads to an identification of the gravitational correlation length appearing in the Wilson loop with an observed large-scale curvature. Our results suggest that strongly coupled gravity leads to a positively curved (De Sitter-like) quantum ground state, implying a positive effective cosmological constant at large distances.