Anisotropic scalar-metric quantum cosmology and unitarity

TL;DR

This paper performs Wheeler-DeWitt quantization of an anisotropic Bianchi I cosmological model with a scalar field, demonstrating that proper mathematical treatment restores unitarity and potentially removes the Big Bang singularity.

Contribution

It introduces a method to restore unitarity in anisotropic quantum cosmology by choosing an appropriate weight factor, addressing a key issue in quantum gravity models.

Findings

Restores unitarity in anisotropic quantum cosmology

Constructs a well-behaved wave function for the universe

Suggests the Big Bang singularity can be avoided in quantum cosmology

Abstract

In this article we perform the Wheeler-DeWitt quantization for Bianchi type $I$ anisotropic cosmological model in the presence of a scalar field minimally coupled to the Einstein-Hilbert gravity theory. We also consider the cosmological (perfect) fluid to construct the matter sector of the model whose dynamics plays the role of time. After obtaining the Wheeler-DeWitt equation from the Hamiltonian formalism, we then define the self-adjointness relations properly. Doing that we proceed to get a solution for the Wheeler-DeWitt equation and construct a well behaved wave function for the universe. The unitary evolution of the wave function in the presence of the scalar field is finally restored by an appropriate choice of weight factor in defining the norm of the wave packet. It is then concluded that the Big-Bang singularity can be removed in the context of quantum cosmology.