Unitary evolution of free massless fields in de Sitter space-time

We consider the quantum dynamics of a massless scalar field in de Sitter space-time. The classical evolution is represented by a canonical transformation on the phase space for the field theory. By studying the corresponding Bogoliubov transformations, we show that the symplectic map that encodes the evolution between two instants of time cannot be unitarily implemented on any Fock space built from a SO(4)-symmetric complex structure. We will show also that, in contrast with some effectively lower dimensional examples arising from Quantum General Relativity such as Gowdy models, it is impossible to find a time dependent conformal redefinition of the massless scalar field leading to a quantum unitary dynamics.Comment: 20 pages. Comments and references adde

Hamiltonian Dynamics of Linearly Polarized Gowdy Models Coupled to Massless Scalar Fields

The purpose of this paper is to analyze in detail the Hamiltonian formulation for the compact Gowdy models coupled to massless scalar fields as a necessary first step towards their quantization. We will pay special attention to the coupling of matter and those features that arise for the three-handle and three-sphere topologies that are not present in the well studied three torus case -in particular the polar constraints that come from the regularity conditions on the metric. As a byproduct of our analysis we will get an alternative understanding, within the Hamiltonian framework, of the appearance of initial and final singularities for these models.Comment: Final version to appear in Classical and Quantum Gravit