  We study in a Brill-Hartle type of approximation the back reaction of a
superposition of linear gravitational waves on the mean gravitational field up
to second order in the wave amplitudes. The background field is taken as an
Einstein-deSitter geometry. In order to follow inflationary scenarios, the
wavelengths are allowed to exceed the temporary Hubble distance. As in optical
coherence theory, the wave amplitudes are considered as random variables, which
form a homogeneous and isotropic stochastic process, sharing the symmetries of
the background metric. The effective stress-energy tensor for the random waves
is calculated in terms of correlation functions and covers subhorizon as well
as superhorizon modes, the latter give in many cases negative contributions to
energy density and pressure. We discuss solutions of the second-order equations
including pure gravitational radiation universes.
