Homogeneous Loop Quantum Cosmology

TL;DR

This paper extends loop quantum cosmology to homogeneous models, simplifying the volume operator and demonstrating singularity-free dynamics in the Bianchi I model.

Contribution

It introduces a diagonalized approach to homogeneous models, enabling explicit spectrum calculation of the volume operator and analysis of the Bianchi I model.

Findings

Volume operator spectrum determined explicitly

Hamiltonian constraint calculated explicitly

Bianchi I model dynamics are singularity-free

Abstract

Loop quantum cosmological methods are extended to homogeneous models in diagonalized form. It is shown that the diagonalization leads to a simplification of the volume operator such that its spectrum can be determined explicitly. This allows the calculation of composite operators, most importantly the Hamiltonian constraint. As an application the dynamics of the Bianchi I model is studied and it is shown that its loop quantization is free of singularities.