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

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.

23 pages. Updated to match published version

References in corpus (15)

• Theory of cosmological perturbations in an anisotropic universe
• Predictions from an anisotropic inflationary era
• Uniqueness of the Fock quantization of the Gowdy $T^3$ model
• Quantum Gowdy $T^3$ model: A uniqueness result
• Quantum Gowdy $T^3$ model: A unitary description
• Uniqueness of the Fock quantization of scalar fields in spatially flat cosmological spacetimes
• Unique Fock quantization of scalar cosmological perturbations
• Quantum Gowdy $T^3$ Model: Schrodinger Representation with Unitary Dynamics
• The TT, TB, EB and BB correlations in anisotropic inflation
• Uniqueness of the Fock quantization of fields with unitary dynamics in nonstationary spacetimes
• Uniqueness of the Fock representation of the Gowdy $S^1\times S^2$ and $S^3$ models
• Uniqueness of the Fock quantization of scalar fields under mode preserving canonical transformations varying in time
• Dirac fields in flat FLRW cosmology: Uniqueness of the Fock quantization
• Inflationary Perturbations in Anisotropic, Shear-Free Universes
• Uniqueness of the Fock quantization of scalar fields and processes with signature change in cosmology

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• A Brief Overview of Results about Uniqueness of the Quantization in Cosmology
• Uniqueness Criteria for the Fock Quantization of Dirac Fields and Applications in Hybrid Loop Quantum Cosmology
• Expansion-sensitive coupling of a local quantum system in de Sitter cosmology