Minisuperspace quantum supersymmetric cosmology (and its hidden hyperbolic Kac-Moody structures)

TL;DR

This paper explores the quantization of N=1, d=4 supergravity in a Bianchi IX cosmological model, revealing a complete solution space, hints of a hidden Kac-Moody algebra, and potential singularity avoidance in the universe's wave function.

Contribution

It provides a comprehensive solution space, uncovers possible hyperbolic Kac-Moody structures, and suggests mechanisms for avoiding cosmological singularities.

Findings

Complete solution space for the model

Evidence of hidden Kac-Moody algebra

Indications of singularity avoidance in wave function

Abstract

This work summarises recent progress obtained by the mini-superpspace quantization of $\mathcal N=1$, $d=4$ supergravity, formulated in the framework of the Bianchi IX cosmological model. The emphasis is put on three main results : the completeness of the solution space obtained, the elements suggesting a hidden Kac-Moody structure of the theory and those leading to conjecture an avoidance of the cosmological singularity by some branches of the wave function of the Universe.