Loop quantum cosmology of Bianchi type II models

Abstract

The improved dynamics of loop quantum cosmology is extended to include the Bianchi type II model. Because these space-times admit both anisotropies and non-zero 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=+/-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 space-like singularities in classical general relativity.