Quantum cosmology in an anisotropic n-dimensional universe

TL;DR

This paper explores quantum cosmological models in an n-dimensional anisotropic universe with a scalar field, analyzing classical solutions and quantum effects on the universe's evolution, especially the behavior of extra dimensions.

Contribution

It introduces quantum cosmological models in an anisotropic n-dimensional setting using a scalar-tensor theory, extending classical models with quantum analysis of universe evolution.

Findings

Classical solutions include a universe with an initial singularity and a static universe.

Quantum effects potentially influence the early universe's evolution.

Extra dimensions tend to shrink over time in the models.

Abstract

We investigate quantum cosmological models in an n-dimensional anisotropic universe in the presence of a massless scalar field. Our basic inspiration comes from Chodos and Detweiler's classical model which predicts an interesting behaviour of the extra dimension, shrinking down as time goes by. We work in the framework of a recent geometrical scalar-tensor theory of gravity. Classically, we obtain two distinct type of solutions. One of them has an initial singularity while the other represents a static universe considered as a whole. By using the canonical approach to quantum cosmology, we investigate how quantum effects could have had an influence in the past history of these universes.