Inflation in an Inhomogeneous Cosmology

We present results on the non-linear dynamics of a wide class of inhomogeneous cosmological models with irrotational dust and vanishing magnetic part of the Weyl tensor, with a cosmological constant Lambda > 0. The study of these models is relevant for the early universe: we find that there are expanding regions that inflate and finally isotropize, i.e. de Sitter is the unique attractor for expansion. There are however regions that can recollapse, even after an inflationary phase. In this case Lamda becomes negligible, and the attractor is the same as for Lamda=0 case: we find that collapsing regions always fall in Kasner-like spindle singularitie