Extra-Dimensional de Broglie-Bohm Quantum Cosmology

TL;DR

This paper investigates how extra dimensions in an anisotropic n-dimensional universe can be dynamically stabilized through quantum cosmology using the de Broglie-Bohm approach, revealing two distinct compactification scenarios.

Contribution

It introduces a quantum cosmology model with a Gaussian wave function that demonstrates dynamical stabilization of extra dimensions in an anisotropic universe.

Findings

Extra dimensions can be stabilized via quantum effects.

Two distinct compactification scenarios are identified.

The five-dimensional case shows degeneracy in the Wheeler-DeWitt equation.

Abstract

In this work, we explore the de Broglie-Bohm Quantum Cosmology for a stiff matter, $p = \rho$, anisotropic n-dimensional Universe. One begins by considering a Gaussian wave function for the Universe, which depends on the momenta parameters $q_1$ and $q_2$ , in addition to the dispersion parameters $\sigma_1$ and $\sigma_2$. Our solutions show that the extra dimensions are stabilized through a dynamical compactification mechanism within the quantum cosmology framework. In this case, we find two distinct configurations for the dynamics of the extra dimensions. The first configuration features larger extra dimensions at the bounce, which subsequently undergo compactification to a smaller size. In contrast, the second configuration exhibits a smaller extra dimension at the bounce, evolving toward a larger, finite, and stabilized value. We also address the particular five-dimensional case where the Wheeler-DeWitt equation degenerates.