Approximative Methods in Inhomogeneous Loop Quantum Cosmology

Abstract

A complete quantization of an approximately homogeneous and isotropic universe with small scalar perturbations is carried out by means of an hybrid approach in Loop Quantum Cosmology. The matter content is provided by a minimally coupled massive scalar field. The homogenous sector of the geometry degrees of freedom is polymerically quantized while the inhomogeneities are quantized employing Fock techniques. The Fock quantization adopted is a privileged one picked out in a unique way by criteria of dynamical unitarity and symmetry invariance in the context of quantum field theory in curved spacetimes. We propose a prescription for the representation of the Hamiltonian constraint as an operator on the kinematical Hilbert space and show how to characterize its solutions by their data on the minimum volume section in each super-selection sector of the theory.