A Toy Model Approach to the Canonical Non-perturbative Quantization of the Spatially Flat Robertson-Walker Spacetimes with Cosmological Constant
Abstract
We present a toy model approach to the canonical non-perturbative quantization of the spatially-flat Robertson-Walker Universes with cosmological constant, based on the fact that such models are exactly solvable within the framework of a simple Lagrangian formulation. The essential quantum dynamical metric-field and the corresponding Hamiltonian, explicitly derived in terms of annihilation and creation operators, point out that the Wheeler - DeWitt equation is a natural (quantum) generalization of the $G_{44}$ - Einstein equation for the classical De Sitter spacetime and selects the physical states of the quantum De Sitter Universe. As a result of the exponential universal expansion, the usual Fock states (defined as the eigenstates of the number-operator) are no longer invariant under the derived Hamiltonian. They exhibit quantum fluctuation of the energy and of the metric field which lead to a (geometrical) volume quantization.
- Publication:
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arXiv e-prints
- Pub Date:
- June 1995
- DOI:
- 10.48550/arXiv.gr-qc/9506051
- arXiv:
- arXiv:gr-qc/9506051
- Bibcode:
- 1995gr.qc.....6051D
- Keywords:
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- General Relativity and Quantum Cosmology
- E-Print:
- 22 pages, LaTex