Gravitational Wilson loop and large scale curvature

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 local averages over loop bivectors, and over lattice rotations, using an assumed near-uniform measure in group space. We then relate the resulting quantum averages to an expected semiclassical 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