STOCHASTIC DYNAMICS OF COARSE-GRAINED QUANTUM-FIELDS IN THE INFLATIONARY UNIVERSE

It is shown how coarse graining of quantum field theory in de Sitter space leads to the emergence of a classical stochastic description as an effective theory in the infrared regime. The quantum state of the coarse-grained scalar field is found to be a highly squeezed coherent state, whose center performs a random walk on a bundle of classical trajectories.