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Loop Quantum Cosmology in Bianchi Type I Models: Analytical Investigation

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arxiv gr-qc/0609029 v4 pith:FWISLOOZ submitted 2006-09-07 gr-qc

Dah-Wei Chiou This is my paper · ORCID
classification gr-qc
keywords cosmologybianchiconstructeddifferenceequationevolutionhilbertinvestigation
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The comprehensive formulation for loop quantum cosmology in the spatially flat, isotropic model was recently constructed. In this paper, the methods are extended to the anisotropic Bianchi I cosmology. Both the precursor and the improved strategies are applied and the expected results are established: (i) the scalar field again serves as an internal clock and is treated as emergent time; (ii) the total Hamiltonian constraint is derived by imposing the fundamental discreteness and gives the evolution as a difference equation; and (iii) the physical Hilbert space, Dirac observables and semi-classical states are constructed rigorously. It is also shown that the state in the kinematical Hilbert space associated with the classical singularity is decoupled in the difference evolution equation, indicating that the big bounce may take place when any of the area scales undergoes the vanishing behavior. The investigation affirms the robustness of the framework used in the isotropic model by enlarging its domain of validity and provides foundations to conduct the detailed numerical analysis.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. On the dynamics of single-vertex states in quantum-reduced loop gravity

    gr-qc 2024-12 conditional novelty 6.0 of 10

    The Hamiltonian of single-vertex states in quantum-reduced loop gravity formally matches Bianchi I loop quantum cosmology, and an analogy suggests adding a non-trivial Lorentzian curvature term to the cosmology Hamiltonian.

  2. Quantum-reduced loop gravity: New perspectives on the kinematics and dynamics

    gr-qc 2024-12 conditional novelty 5.0 of 10

    The paper reformulates quantum-reduced loop gravity with a master constraint operator and finds that its single-node Hamiltonian matches the Bianchi I loop quantum cosmology Hamiltonian.

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