Restoring unitarity in anisotropic quantum cosmological models

Abstract

The present work shows that a properly chosen ordering of operators can restore unitarity in anisotropic quantum cosmological models. Bianchi V and Bianchi IX models with a perfect fluid are worked out. A transformation of coordinates takes the Hamiltonian to that of an inverse square potential which has equal deficiency indices; thus, a self-adjoint extension is possible. Although not clearly detected before, we show here that isotropic models are also apt to violate the conservation of probability for careless operator ordering.