Homogeneous Loop Quantum Cosmology: The Role of the Spin Connection
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Homogeneous cosmological models with non-vanishing intrinsic curvature require a special treatment when they are quantized with loop quantum cosmological methods. Guidance from the full theory which is lost in this context can be replaced by two criteria for an acceptable quantization, admissibility of a continuum approximation and local stability. A quantization of the corresponding Hamiltonian constraints is presented and shown to lead to a locally stable, non-singular evolution compatible with almost classical behavior at large volume. As an application, the Bianchi IX model and its modified behavior close to its classical singularity is explored.
revtex4, 36 pages, 10 figures. In version 2 the introduction is expanded, section III E is added and a paragraph on relevance of results is added in the conclusions. Refs updated, results unchanged. To appear in Class. Quant. Gravity
revtex4, 36 pages, 10 figures. In version 2 the introduction is expanded, section III E is added and a paragraph on relevance of results is added in the conclusions. Refs updated, results unchanged. To appear in Class. Quant. Gravity