Quantum cosmology of 5D non-compactified Kaluza-Klein theory

TL;DR

This paper explores the quantum cosmology of a five-dimensional non-compactified Kaluza-Klein model, revealing how the Vilenkin wave function predicts the universe's emergence on a specific hypersurface, with implications for understanding higher-dimensional cosmology.

Contribution

It introduces a quantum cosmological model with a 5D non-compactified Kaluza-Klein framework and demonstrates the utility of the Vilenkin wave function in predicting universe creation.

Findings

Vilenkin wave function predicts universe emergence at l≈0 hypersurface

Model effectively reduces to a 4D non-minimally coupled dilaton field

Provides insights into higher-dimensional quantum cosmology

Abstract

We study the quantum cosmology of a five dimensional non-compactified Kaluza-Klein theory where the 4D metric depends on the fifth coordinate, $x^4\equiv l$. This model is effectively equivalent to a 4D non-minimally coupled dilaton field in addition to matter generated on hypersurfaces l=constant by the extra coordinate dependence in the four-dimensional metric. We show that the Vilenkin wave function of the universe is more convenient for this model as it predicts a new-born 4D universe on the $l\simeq0$ constant hypersurface.