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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=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.
Ashtekar et al. (Tue,) studied this question.