A Toy Model Approach to the Canonical Nonperturbative Quantization of the Spatially Flat RobertsonWalker Spacetimes with Cosmological Constant
Abstract
We present a toy model approach to the canonical nonperturbative quantization of the spatiallyflat RobertsonWalker 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 metricfield 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 numberoperator) 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:

arXiv eprints
 Pub Date:
 June 1995
 arXiv:
 arXiv:grqc/9506051
 Bibcode:
 1995gr.qc.....6051D
 Keywords:

 General Relativity and Quantum Cosmology
 EPrint:
 22 pages, LaTex