Just some simple (but nontrivial) analytical solutions for de Broglie-Bohm quantum cosmology

TL;DR

This paper presents simple analytical solutions to the Wheeler-DeWitt equation in de Broglie-Bohm quantum cosmology, illustrating specific scalar field potentials and their implications for universe models.

Contribution

It provides new explicit solutions for the Wheeler-DeWitt equation in de Broglie-Bohm quantum cosmology with particular scalar potentials.

Findings

One solution features a Gaussian scale factor with a quadratic potential and negative cosmological constant.

Another solution describes a flat Minkowski universe with a hilltop potential.

Abstract

In this work, we provide some simple analytical solutions to the Wheeler-DeWitt equation for the minisuperspace applied to de Broglie-Bohmian quantum cosmology for particular potentials of a scalar matter field $\phi$. One solution describes a constantly rolling scalar field with a quadratic potential plus a negative cosmological constant. The scale factor is given by a Gaussian function. The other solution describes a flat Minkowski universe with the potential of a hilltop form.