Complete Quantization of Scalar Cosmological Perturbations

Abstract

We quantize a perturbed Friedmann–Lemaître–Robertson–Walker model coupled to a massive scalar field. We consider only scalar perturbations, in a universe whose spatial sections have the topology of a three-sphere. The local gauge freedom is fixed at the classical level. We choose a preferred parametrization of the system by adapting uniqueness criteria for the quantization of scalar fields with time-dependent mass. The Hilbert space of the theory is constructed combining a polymer representation for the homogeneous background and the preferred Fock quantization for the perturbations. Finally, we propose a prescription to promote the Hamiltonian constraint to a quantum operator, and characterize the states annihilated by it in terms of their initial data at the minimum-volume section.