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. In 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. © Copyright EPLA, 2012.
All Science Journal Classification (ASJC) codes
- Physics and Astronomy(all)
Cianfrani, F., Marchini, A., & Montani, G. (2012). The picture of the Bianchi i model via gauge fixing in Loop Quantum Gravity. Europhysics Letters, 99(1), -. . https://doi.org/10.1209/0295-5075/99/10003