On unitary time evolution in gowdy T3 cosmologies

A non-perturbative canonical quantization of the Gowdy T-3 polarized models is considered here. 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 made, for which the true degrees of freedom of the model reduce to a massless free scalar field propagating on a two-dimensional expanding torus. It is shown that the symplectic transformation that determines the classical dynamics cannot be unitarily implemented on the corresponding Hilbert spare of quantum states. The implications of this result for both the quantization of fields on curved manifolds and other physically relevant questions regarding the initial singularity axe discussed.