Unitary evolution for a quantum Kantowski-Sachs cosmology

TL;DR

This paper demonstrates that the Kantowski-Sachs cosmological model admits a unitary quantum evolution, similar to other anisotropic models, and constructs a wave-packet to establish unitarity beyond simple eigenstates.

Contribution

It proves unitarity in the Kantowski-Sachs model through wave-packet construction and shows the Hamiltonian admits a self-adjoint extension, addressing non-unitarity concerns.

Findings

Unitarity is achievable in Kantowski-Sachs quantum cosmology.

Wave-packet superposition confirms non-trivial unitarity.

Hamiltonian admits self-adjoint extension for $ eq1$.

Abstract

It is shown that like Bianchi I, V and IX models, a Kantowski-Sachs cosmological model also allows a unitary evolution on quantization. It has also been shown that this unitarity is not at the expense of the anisotropy. Non-unitarity, if there is any, cannot escape notice in this as the evolution is studied against a properly oriented time parameter fixed by the evolution of the fluid. Furthermore, we have constructed a wave-packet by superposing different energy eigenstates, thereby establishing unitarity in a non-trivial way, which is a stronger result than an energy eigenstate trivially giving time independent probability density. For $\alpha\neq1$, we have proved that the Hamiltonian upon suitable operator ordering admits a self-adjoint extension under reasonable assumption, using a standard theorem. This consolidates the recently shown fact that the problem of non-unitarity cannot be a generic problem of anisotropy.