On Unitary Time Evolution in Gowdy $T^3$ Cosmologies

TL;DR

This paper investigates the non-perturbative quantum dynamics of Gowdy T^3 cosmologies, revealing that the classical evolution cannot be implemented unitarily in the quantum theory, impacting our understanding of quantum gravity and singularities.

Contribution

It demonstrates that the classical symplectic transformation in Gowdy T^3 models cannot be unitarily realized in the quantum framework, highlighting fundamental issues in quantum cosmology.

Findings

Classical dynamics cannot be unitarily implemented in the quantum model.

Implications for quantum field theory on curved spacetimes.

Insights into the quantum nature of cosmological singularities.

Abstract

A non-perturbative canonical quantization of Gowdy $T^3$ polarized models carried out recently is considered. This approach profits from the equivalence between the symmetry reduced model and 2+1 gravity coupled to a massless real scalar field. The system is partially gauge fixed and a choice of internal time is performed, for which the true degrees of freedom of the model reduce to a massless free scalar field propagating on a 2-dimensional expanding torus. It is shown that the symplectic transformation that determines the classical dynamics cannot be unitarily implemented on the corresponding Hilbert space of quantum states. The implications of this result for both quantization of fields on curved manifolds and physically relevant questions regarding the initial singularity are discussed.