Quantum Cosmological Multidimensional Einstein-Yang-Mills Model in a $R \times S^3 \times S^d$ Topology

TL;DR

This paper investigates a quantum cosmological model with multidimensional Einstein-Yang-Mills fields on a topology combining real line and spheres, revealing stable solutions and the influence of extra dimensions on classical and quantum regions.

Contribution

It introduces non-vanishing time-dependent Yang-Mills configurations in both compact spaces and finds stable compactifying solutions within the Hartle-Hawking framework, highlighting the role of extra dimensions.

Findings

Stable compactifying solutions as extrema of the wave function

Dependence of classical/quantum regions on the number of extra dimensions

Yang-Mills fields with non-zero time components in multiple spaces

Abstract

The quantum cosmological version of the multidimensional Einstein-Yang-Mills model in a $R \times S^3 \times S^d$ topology is studied in the framework of the Hartle-Hawking proposal. In contrast to previous work in the literature, we consider Yang-Mills field configurations with non-vanishing time-dependent components in both $S^3$ and $S^d$ spaces. We obtain stable compactifying solutions that do correspond to extrema of the Hartle-Hawking wave function of the Universe. Subsequently, we also show that the regions where 4-dimensional metric behaves classically or quantum mechanically (i.e. regions where the metric is Lorentzian or Euclidean) will depend on the number, $d$, of compact space dimensions.