The “improved dynamics” of loop quantum cosmology is extended to include the Bianchi type II model. Because these space-times admit both anisotropies and nonzero spatial curvature, certain technical difficulties arise over and above those encountered in the analysis of the (anisotropic but spatially flat) Bianchi type I space-times and of the (spatially curved but isotropic) $k=\pm 1$ models. We address these and show that the big-bang singularity is resolved in the same precise sense as in the recent analysis of the Bianchi I model. Bianchi II space-times are of special interest to quantum cosmology because of the expected behavior of the gravitational field near generic spacelike singularities in classical general relativity.

• Received 7 October 2009

DOI:https://doi.org/10.1103/PhysRevD.80.123532