Addressing the issue of non-unitarity in anisotropic quantum cosmology

TL;DR

This paper demonstrates that non-unitarity in anisotropic quantum cosmology models is not inherent, providing examples and operator ordering methods to ensure well-behaved, time-independent wave function norms.

Contribution

It shows that non-unitarity is not a generic issue in anisotropic quantum cosmology and proposes operator ordering as a solution.

Findings

Bianchi-I model with ultrarelativistic fluid has a well-behaved norm

Proper operator ordering yields time-independent norms for wave packets

Non-unitarity is not a fundamental problem in these models

Abstract

In the present work we show that the widely believed pathology of the non-unitarity of anisotropic quantum cosmological models cannot be a generic problem. We exhibit a non trivial example, a Bianchi-I model with an ultrarelativistic fluid, that has a well behaved time independent norm. We also show that a suitable operator ordering should produce time independent norms for the wave packets in the case of other more realistic fluids as well.