  A duality transformation that interrelates expanding and contracting
cosmological models is shown to single out a duality invariant, interacting
two-component description of any irrotational, geodesic and shearfree cosmic
medium with vanishing three curvature scalar. We apply this feature to a system
of matter and radiation, to a mixture of dark matter and dark energy, to
minimal and conformal scalar fields, and to an enlarged Chaplygin gas model of
the cosmic substratum. We extend the concept of duality transformations to
cosmological perturbations and demonstrate the invariance of adiabatic pressure
perturbations under these transformations.
