Unitary evolution for a quantum Kantowski–Sachs cosmology

It is shown that like the Bianchi I, V and IX models, a Kantowski–Sachs cosmological model also allows unitary evolution on quantization. It has also been shown that this unitarity is not at the expense of anisotropy. Non-unitarity, if there is any, cannot escape notice here, 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 a time independent probability density. For $\alpha \ne 1$, we have proved that the Hamiltonian admits a self-adjoint extension under a reasonable assumption, using a standard theorem. This consolidates the fact that the problem of non-unitarity cannot be a generic problem of anisotropy. (paper)