Quantization of the Bianchi type-IX model in N=1 Supergravity in the Presence of Supermatter

TL;DR

This paper explores the quantization of the Bianchi type-IX cosmological model within N=1 supergravity, incorporating supermatter fields, and derives new solutions to the quantum constraints under different potential conditions.

Contribution

It introduces a novel analysis of supermatter effects in Bianchi type-IX supergravity models, providing explicit solutions for the wave function of the universe.

Findings

Wave function simplifies without potential terms.

New solutions for quantum constraints are obtained.

Analysis distinguishes cases with and without analytical potentials.

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 K\"ahler geometry is chosen to be a two-dimensional flat one. The Lorentz invariant Ansatz for the wave function of the universe is taken to be as simple as possible in order to obtain {\it new} solutions. The set of differential equations derived from the quantum constraints are analysed in two different cases: if the supermatter terms include an analytical potential or not. In the latter the wave function is found to have a simple form.