$\rm \Psi= W e^{\pm \Phi}$ quantum cosmological solutions for Class A Bianchi Models

TL;DR

This paper derives new quantum cosmological solutions for Class A Bianchi models, extending previous work and highlighting differences with supersymmetric approaches, particularly for Bianchi II and IX models.

Contribution

It generalizes existing quantum cosmology solutions for Class A Bianchi models using a specific exponential form, revealing unique solutions for Bianchi II and IX.

Findings

Solutions of the form Ψ=W e^{± Φ} for quantum Bianchi models

Identification of special solutions where Ψ must be zero for Bianchi II and IX

Differences observed compared to supersymmetric quantum cosmology

Abstract

We find solutions for quantum Class A Bianchi models of the form $\rm \Psi=W e^{\pm \Phi}$ generalizing the results obtained by Moncrief and Ryan in standard quantum cosmology. For the II and IX Bianchi models there are other solutions $\rm \tilde\Phi_2$, $\rm \tilde\Phi_9$ to the Hamilton-Jacobi equation for which $\rm \Psi$ is necessarely zero, in contrast with solutions found in supersymmetric quantum cosmology.