Reduced density matrices and decoherence in quantum cosmology

We investigate a quantum cosmological model consisting of inhomogeneous massless minimally coupled scalar field perturbations on a closed Friedmann-Robertson-Walker minisuperspace model with a spatially homogeneous massless minimally coupled scalar field. We discuss how to define a reduced density matrix by summing over the perturbations in the full density matrix, using the approximate Hilbert-space structure that exists for the perturbation wave function when the minisuperspace part of the wave function is of the WKB form. We then concentrate on two particular candidates for a reduced density matrix and discuss their relation to particle creation effects in quantum field theory on curved spacetime. Our results do not suggest that decoherence in the reduced density matrices could be directly identified as a lack of interference between the classical trajectories that correspond to a WKB minisuperspace part of the total wave function.