Smoothing Out Spatially Closed Cosmologies

We discuss a smoothing-out procedure that deforms a family of locally inhomogeneous and anisotropic spatially closed cosmological models into closed Friedmann-Robertson-Walker universes. This gives a precise content to the averaging hypothesis tacitly assumed in cosmology by providing explicitly the correction terms to the physical sources induced on smoothing out the space-time geometry. The consequences of such terms on the dynamics of the Universe are discussed.