Fermionic quantum cosmology as a framework for resolving type IV singularities

TL;DR

This paper introduces a novel fermionic quantum cosmology framework using the Eisenhart-Duval lift and Dirac equation solutions to address and resolve type IV singularities, demonstrating potential for singularity regularization.

Contribution

It develops a new approach combining Eisenhart-Duval lift and Dirac equations in quantum cosmology to effectively resolve type IV singularities.

Findings

Quantum regularization of classical singularity achieved.

Fermionic degrees of freedom incorporated into cosmological models.

Solutions expressed in hypergeometric and Laguerre functions.

Abstract

In this paper, we present an innovative approach to resolving type IV singularities in fermionic quantum cosmology. The Eisenhart-Duval lift procedure is employed to construct an extended minisuperspace metric, which allows for the formulation of the Dirac equation in minisuperspace. Through this approach, fermionic degrees of freedom are effectively incorporated into a homogeneous and isotropic cosmological model with a scalar field. By applying a kind of the Born-Oppenheimer approximation, solutions to the Dirac equation for an approximate potential characteristic of type IV singularities are obtained, expressed in terms of Tricomi confluent hypergeometric functions and associated Laguerre polynomials. The elimination of non-physical, divergent solutions results in a quantum regularization of the classical singularity. These results indicate the potential of fermionic models in quantum cosmology for mitigating the singularity problem.