Uniqueness of the Fock quantization of scalar fields in a Bianchi I cosmology with unitary dynamics

TL;DR

This paper proves the uniqueness of Fock quantization for scalar fields in Bianchi I cosmology by extending criteria of symmetry and unitarity of dynamics, ensuring a consistent quantum description in anisotropic spacetimes.

Contribution

It generalizes the uniqueness results of Fock quantization from isotropic to anisotropic Bianchi I cosmologies using unitarity and symmetry criteria.

Findings

Uniqueness of Fock representation established for Bianchi I models.

Criteria of unitarity and symmetry suffice to select a unique quantization.

Results extend previous isotropic case to anisotropic, shear-containing spacetimes.

Abstract

The Fock quantization of free scalar fields is subject to an infinite ambiguity when it comes to choosing a set of annihilation and creation operators, choice that is equivalent to the determination of a vacuum state. In highly symmetric situations, this ambiguity can be removed by asking vacuum invariance under the symmetries of the system. Similarly, in stationary backgrounds, one can demand time-translation invariance plus positivity of the energy. However, in more general situations, additional criteria are needed. For the case of free (test) fields minimally coupled to a homogeneous and isotropic cosmology, it has been proven that the ambiguity is resolved by introducing the criterion of unitary implementability of the quantum dynamics, as an endomorphism in Fock space. This condition determines a specific separation of the time dependence of the field, so that this splits into a very precise background dependence and a genuine quantum evolution. Furthermore, together with the condition of vacuum invariance under the spatial Killing symmetries, unitarity of the dynamics selects a unique Fock representation for the canonical commutation relations, up to unitary equivalence. In this work, we generalize these results to anisotropic spacetimes with shear, which are therefore not conformally symmetric, by considering the case of a free scalar field in a Bianchi I cosmology.