  We consider an extension of WDW minisuperpace cosmology with additional
interaction terms that preserve the linear structure of the theory. General
perturbative methods are developed and applied to known semiclassical solutions
for a closed Universe filled with a massless scalar. The exact Feynman
propagator of the free theory is derived by means of a conformal transformation
in minisuperspace. As an example, a stochastic interaction term is considered
and first order perturbative corrections are computed. It is argued that such
an interaction can be used to describe the interaction of the cosmological
background with the microscopic d.o.f. of the gravitational field. A
Helmoltz-like equation is considered for the case of interactions that do not
depend on the internal time and the corresponding Green's kernel is obtained
exactly.The possibility of linking this approach to fundamental theories of
Quantum Gravity is investigated.
