  Canonical methods of quasiclassical dynamics make it possible to go beyond a
strict background approximation for cosmological perturbations by including
independent fields such as correlation degrees of freedom. New models are
introduced and analyzed here for cosmological dynamics in the presence of
quantum correlations between background and perturbations, as well as
cross-correlations between different modes of a quantum field. Evolution
equations for moments of a perturbation state reveal conditions required for
inhomogeneity to build up out of an initial vacuum. A crucial role is played by
quantum non-locality, formulated by canonical methods as an equivalent local
theory with non-classical degrees of freedom given by moments of a quantum
state.
