Troubles with quantum anistropic cosmological models: Loss of unitarity

TL;DR

This paper investigates the quantization of an anisotropic cosmological model, revealing that the resulting quantum theory loses unitarity due to the Hamiltonian's mathematical properties, affecting the predictability of cosmological scenarios.

Contribution

It demonstrates the loss of unitarity in the quantum Bianchi I model with perfect fluid, highlighting issues related to the Hamiltonian's self-adjointness in anisotropic quantum cosmology.

Findings

Wave function norm is time-dependent, indicating non-unitarity.

The Hamiltonian is hermitian but not self-adjoint, causing unitarity loss.

Different cosmological predictions arise from expectation values and Bohmian trajectories.

Abstract

The anisotropic Bianchi I cosmological model coupled with perfect fluid is quantized in the minisuperspace. The perfect fluid is described by using the Schutz formalism which allows to attribute dynamical degrees of freedom to matter. A Schr\"odinger-type equation is obtained where the matter variables play the role of time. However, the signature of the kinetic term is hyperbolic. This Schr\"odinger-like equation is solved and a wave packet is constructed. The norm of the resulting wave function comes out to be time dependent, indicating the loss of unitarity in this model. The loss of unitarity is due to the fact that the effective Hamiltonian is hermitian but not self-adjoint. The expectation value and the bohmian trajectories are evaluated leading to different cosmological scenarios, what is a consequence of the absence of a unitary quantum structure. The consistency of this quantum model is discussed as well as the generality of the absence of unitarity in anisotropic quantum models.