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

Abstract

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.

20 pages. Comments and references added

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Cited by in corpus (6)

• Unitarity and ultraviolet regularity in cosmology
• The time-dependent quantum harmonic oscillator revisited: Applications to Quantum Field Theory
• Quantum unitary evolution of linearly polarized S^1\times S^2 and S^3 Gowdy models coupled to massless scalar fields
• Quantum Cosmological Perturbations of Multiple Fluids
• Uniqueness of the Fock quantization of scalar fields and processes with signature change in cosmology
• Bogoliubov Transformation and Schrodinger Representation on Curved Space