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

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

2012-01-12

arxiv.org/abs/1201.2588v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

6 pages

Scientific paper

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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