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arXiv · 1201.2588

The picture of the Bianchi I model via gauge fixing in Loop Quantum Gravity

Francesco Cianfrani·Andrea Marchini·Giovanni Montani
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Abstract

The implications of the SU(2) gauge fixing associated with the choice of invariant triads in Loop Quantum Cosmology are discussed for a Bianchi I model. In particular, via the analysis of Dirac brackets, it is outlined how the holonomy-flux algebra coincides with the one of Loop Quantum Gravity if paths are parallel to fiducial vectors only. This way the quantization procedure for the Bianchi I model is performed by applying the techniques developed in Loop Quantum Gravity but restricting the admissible paths. Furthermore, the local character retained by the reduced variables provides a relic diffeomorphisms constraint, whose imposition implies homogeneity on a quantum level. The resulting picture for the fundamental spatial manifold is that of a cubical knot with attached SU(2) irreducible representations. The discretization of geometric operators is outlined and a new perspective for the super-Hamiltonian regularization in Loop Quantum Cosmology is proposed.

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Francesco Cianfrani, Andrea Marchini, Giovanni Montani. 2012-01-12. The picture of the Bianchi I model via gauge fixing in Loop Quantum Gravity. https://doi.org/10.1209/0295-5075%2F99%2F10003

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