  The canonical quantum theory of gravity -- Quantum Geometrodynamics (QG) is
applied to the homogeneous Bianchi type IX cosmological model. As a result, the
framework for the quantum theory of homogeneous cosmologies is developed. We
show that the theory is internally consistent, and prove that it possesses the
correct classical limit (the theory of general relativity). To emphasize the
special role that the constraints play in this new theory we, compare it to the
traditional ADM square-root and Wheeler-DeWitt quantization schemes. We show
that, unlike the traditional approaches, QG leads to a well-defined Schrodinger
equation for the wave-function of the universe that is inherently coupled to
the expectation value of the constraint equations. This coupling to the
constraints is responsible for the appearance of a coherent spacetime picture.
Thus, the physical meaning of the constraints of the theory is quite different
from Dirac's interpretation. In light of this distinctive feature of the
theory, we readdress the question of the dark energy effects in the Bianchi IX
cosmological model for highly non-classical quantum states. We show that, at
least for this model, for any choice of the initial wave function, the quantum
corrections will not produce the accelerated expansion of the universe.
