  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.
