Quantum fluctuations as the cause of inhomogeneity in the universe

In this paper the authors consider the canonical quantization of a cosmological model without any assumptions of homogeneity or isotropy. They treat the two homogeneous and isotropic degrees of freedom of the gravitational and matter fields exactly and the other degrees of freedom to second order in the Hamiltonian. They derive a background Wheeler DeWitt equation for the two homogenous isotropic degrees of freedom and time dependent Schroedinger equations for the other degrees of freedom which are treated as perturbations on the background. The authors assume that the universe is in the quantum state defined by a path integral over compact metrics. They justify their treatment of the inhomogeneous modes to second order only by showing that they start out in their ground states