Loop Quantum Cosmology of non-diagonal Bianchi models

TL;DR

This paper develops a loop quantum cosmology framework for non-diagonal Bianchi models, extending previous diagonal models, and shows that key quantum geometric features are preserved in the non-diagonal Bianchi I case.

Contribution

It provides a classical and quantum formulation of non-diagonal Bianchi models within loop quantum gravity, highlighting invariance properties in the Bianchi I case.

Findings

Loop quantization of non-diagonal Bianchi models achieved.

Geometrical operators are invariant in the Bianchi I case.

Kinematical Hilbert space similar to diagonal models.

Abstract

The non-diagonal Bianchi models are studied in the loop framework for their classical and quantum formulation. The expressions of the Ashtekar-Barbero-Immirzi variables and their properties are found to provide a loop quantization of these models. In the special case of Bianchi I Universe, it is shown that the geometrical operators result invariant from the diagonal description. Hence, the kinematical Hilbert space of the non-diagonal Bianchi I model has similar features to the diagonal one.