Unitarity in quantum cosmology: symmetries protected and violated

TL;DR

This paper investigates how the self-adjoint extension of the Hamiltonian affects symmetry preservation in quantum Bianchi I cosmology, revealing loss of scale invariance but preservation of Noether symmetries, thus addressing unitarity issues.

Contribution

It demonstrates the conditions under which symmetries are preserved or violated in quantum cosmology with self-adjoint Hamiltonian extensions.

Findings

Scale invariance is lost in the quantum model.

Noether symmetries are preserved despite Hamiltonian extension.

Unitarity is ensured through self-adjoint extension of the Hamiltonian.

Abstract

This work deals with the violation or retention of symmetries associated with the self-adjoint extension of the Hamiltonian for homogeneous but anisotropic Bianchi I cosmological model. This extension is required to make sure the quantum evolution is unitary. It is found that the scale invariance is lost, but the Noether symmetries are preserved.