  For general relativistic spacetimes filled with an irrotational perfect fluid
a generalized form of Friedmann's equations governing the expansion factor of
spatially averaged portions of inhomogeneous cosmologies is derived. The
averaging problem for scalar quantities is condensed into the problem of
finding an `effective equation of state' including kinematical as well as
dynamical `backreaction' terms that measure the departure from a standard FLRW
cosmology. Applications of the averaged models are outlined including
radiation-dominated and scalar field cosmologies (inflationary and
dilaton/string cosmologies). In particular, the averaged equations show that
the averaged scalar curvature must generically change in the course of
structure formation, that an averaged inhomogeneous radiation cosmos does not
follow the evolution of the standard homogeneous-isotropic model, and that an
averaged inhomogeneous perfect fluid features kinematical `backreaction' terms
that, in some cases, act like a free scalar field source. The free scalar field
(dilaton) itself, modelled by a `stiff' fluid, is singled out as a special
inhomogeneous case where the averaged equations assume a simple form.
