Supersymmetric quantum cosmology proposals and the Bianchi type-II model

Abstract

Using the hidden symmetry method, we compare it to the two other proposals for supersymmetric quantum cosmology and show that even when they are not equivalent, they give similar wave functions for the FRW k=+1 model and the microsuperspace sector of the Taub model. In particular, this hidden symmetry method is extended to the Bianchi type-II model finding the full expansion for \ensuremath{\Psi}. This contains terms satisfying the no-boundary proposal of Hartle and Hawking but also terms behaving as proposed by Hawking for quantum wormhole states. Demanding that \ensuremath{\Psi} does not diverge for \ensuremath{\Vert}x\ensuremath{\Vert},\ensuremath{\Vert}y\ensuremath{\Vert}->\ensuremath{\infty}, and at fixed \ensuremath{\alpha}, then the nonbosonic terms could determine the behavior of \ensuremath{\Vert}\ensuremath{\Psi}${\mathrm{\ensuremath{\Vert}}}^{2}$, differing deeply with respect to the behavior caused by the purely bosonic first term.