Quantum unitary evolution of linearly polarized S^1\times S^2 and S^3 Gowdy models coupled to massless scalar fields

Abstract

The purpose of this paper is to study in detail the problem of defining unitary evolution for linearly polarized S^1 x S^2 and S^3 Gowdy models (in vacuum or coupled to massless scalar fields). We show that in the Fock quantizations of these systems no choice of acceptable complex structure leads to a unitary evolution for the original variables. Nonetheless, unitarity can be recovered by suitable redefinitions of the basic fields. These are dictated by the time dependent conformal factors that appear in the description of the standard deparameterized form of these models as field theories in certain curved backgrounds. We also show the unitary equivalence of the Fock quantizations obtained from the SO(3)-symmetric complex structures for which the dynamics is unitarily implemented.

Final version to appear in Classical and Quantum Gravity

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• Uniqueness of the Fock quantization of scalar fields and processes with signature change in cosmology
• A Brief Overview of Results about Uniqueness of the Quantization in Cosmology
• Unitary evolution of free massless fields in de Sitter space-time
• Schrodinger quantization of linearly polarized Gowdy $S^1\times S^2$ and $S^3$ models coupled to massless scalar fields
• Bogoliubov Transformation and Schrodinger Representation on Curved Space
• Inflation from inhomogeneous polarized Gowdy model