  The derivation of the angular spectrum of temperature perturbations of the
cosmic microwave background relies on the quantization of field and metric
perturbations in the inflationary phase. The quantization procedure thus
deserves a close examination. As the background spacetime on which the degrees
of freedom that are quantized live is curved, the methods of quantum field
theory in curved spacetimes are applicable. Furthermore the dynamic system that
is quantized contains a constraint, which adds an interesting problem to the
quantization of the system. This article investigates the treatment of the
constraints and the Weyl quantization of the system. A preferred quantization
procedure is identified, which renders the field and metric perturbations
non-local.
