Quantum BPS Cosmology

TL;DR

This paper develops a quantum cosmology model using the BPS equation instead of the Wheeler-DeWitt equation, allowing for a conserved probability current and exploring classical and quantum properties of scalar fields.

Contribution

It introduces a novel quantum cosmology approach based on the BPS equation, expanding the tools for understanding early universe initial conditions.

Findings

Constructed a wave function and probability distribution using the BPS equation.

Demonstrated the existence of a conserved probability current in the model.

Analyzed classical and quantum behaviors of Dirac-Born-Infeld scalar fields.

Abstract

There has been much discussion about the initial conditions of the early Universe in the context of quantum theory. In this paper, we construct the wave function and probability distribution by adopting the quantum version of the BPS equation instead of the usual Wheeler-DeWitt equation in a minisuperspace quantum cosmology with spatially uniform scalar fields. Although the model treated in this study is technically valid for a limited form of scalar potential, we show that it is possible to construct a conserved probability current in our model. We also examine classical and quantum aspects of models with the Dirac-Born-Infeld type scalar fields.