Quantum Geometrodynamics of the Bianchi IX cosmological model

TL;DR

This paper develops a consistent quantum geometrodynamics framework for the Bianchi IX cosmological model, leading to a Schrödinger equation coupled to constraints, and investigates quantum effects on cosmic acceleration.

Contribution

It introduces a new quantum theory of homogeneous cosmologies with a well-defined Schrödinger equation coupled to constraints, differing from traditional approaches.

Findings

The theory is internally consistent and has the correct classical limit.

Quantum corrections do not induce accelerated expansion in the Bianchi IX model.

The constraints have a different physical interpretation than in Dirac's approach.

Abstract

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.