Back to Basics?... or How can supersymmetry be used in simple quantum cosmological model

TL;DR

This paper explores the application of N=1 supergravity with supermatter to a Bianchi IX quantum cosmological model, seeking simple wave function solutions and examining their properties in the context of supersymmetry.

Contribution

It introduces a simple wave function Ansatz for a supergravity quantum cosmological model and analyzes its solutions, contrasting with more general approaches.

Findings

Wave function solutions are obtained when potential energy is zero.

Wormhole and Hartle-Hawking states are not found in this framework.

The simple Ansatz provides new insights into supersymmetric quantum cosmology.

Abstract

The general theory of N=1 supergravity with supermatter is applied to a Bianchi type IX diagonal model. The supermatter is constituted by a complex scalar field and its spin-$1\over 2$ fermionic partners. The Lorentz invariant Ansatz for the wave function of the universe, $\Psi$, is taken to be as simple as possible in order to obtain {\it new} solutions. The wave function has a simple form when the potential energy term is set to zero. However, neither the wormhole or the Hartle-Hawking state could be found. The Ansatz for $\Psi$ used in this paper is constrasted with the more general framework of R. Graham and A. Csord\'as.