Loop quantum cosmology of Bianchi IX: Inclusion of inverse triad corrections

Abstract

We consider the loop quantization of the (diagonal) Bianchi type IX cosmological model. We explore different quantization prescriptions that extend the work of Wilson-Ewing and Singh. In particular, we study two different ways of implementing the so-called inverse triad corrections. We construct the corresponding Hamiltonian constraint operators and show that the singularity is formally resolved. We find the effective equations associated with the different quantization prescriptions, and study the relation with the isotropic $k$=1 model that, classically, is contained within the Bianchi IX model. We use geometrically defined scalar observables to explore the physical implications of each of these theories. This is the first part in a series of papers analyzing different aspects of the Bianchi IX model, with inverse corrections, within loop quantum cosmology.

18 pages, 2 figures. Prepared for the special issue on Loop Quantum Cosmology of the International Journal of Modern Physics D

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• Generic absence of strong singularities in loop quantum Bianchi-IX spacetimes
• An Overview on the Nature of the Bounce in LQC and PQM
• Loop Quantum Cosmology: A brief review
• Implications of quantum ambiguities in k=1 loop quantum cosmology: distinct quantum turnarounds and the super-Planckian regime
• Open problems in mathematical physics
• Loop Quantum Cosmology: Physics of Singularity Resolution and its Implications