Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
1995-06-23
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
22 pages, LaTex
Scientific paper
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.
Dariescu Ciprian
Dariescu Marina--Aura
Hamamoto Shinji
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