Quantum Geometrodynamics of the Bianchi IX Cosmological Model
The canonical quantum theory of gravity?quantum geometrodynamics (QG)?is applied to the homogeneous Bianchi type IX cosmological model. As a result, a 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 traditional approaches, QG leads to a well-defined Schr?dinger equation for the wavefunction 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 re-address 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 wavefunction, quantum corrections will not produce accelerated expansion of the universe.