  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.
