Quantization of Perturbations in Inflation

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.