Loop quantum cosmology of Bianchi type II models

Absence of preclassical solutions in Bianchi I loop quantum cosmology.

Loop quantum cosmology, the symmetry reduction of quantum geometry for the study of various cosmological situations, leads to a difference equation for its quantum evolution equation. To ensure that solutions of this equation act in the expected classical manner far from singularities, additional restrictions are imposed on the solution. In this Letter, we consider the Bianchi I model, both the...

The Bianchi IX model in Loop Quantum Cosmology

Martin Bojowald, ∗ Ghanashyam Date, † and Golam Mortuza Hossain ‡ Max-Planck-Institut für Gravitationsphysik, Albert-Einstein-Institut, Am Mühlenberg 1, D-14476 Golm, Germany The Institute of Mathematical Sciences CIT Campus, Chennai-600 113, INDIA. Abstract The Bianchi IX model has been used often to investigate the structure close to singularities of general relativity. Its classical chaos is...

Towards inhomogeneous loop quantum cosmology: triangulating Bianchi IX with perturbations

Bianchi-type string cosmology

Bianchi-type string cosmology involves generalizations of the FRW backgrounds with three transitive spacelike Killing symmetries, but without any a priori assumption of isotropy in the 3D sections of homogeneity. With emphasis on those cases with diagonal metrics and vanishing cosmological constant which have not been previously examined in the literature, the present findings allow an overview...

Loop Quantum Cosmology II: Volume Operators

Volume operators measuring the total volume of space in a loop quantum theory of cosmological models are constructed. In the case of models with rotational symmetry an investigation of the Higgs constraint imposed on the reduced connection variables is necessary, a complete solution of which is given for isotropic models; in this case the volume spectrum can be calculated explicitly. It is obse...