A local view of the observable universe

We present results on the nonlinear dynamics of inhomogeneous cosmological models with irrotational dust and a positive cosmological constant, considering, in particular, a wide class with vanishing magnetic Weyl tensor. We find that de Sitter is the unique attractor for those patches of the Universe that are able to expand (cosmic no-hair theorem). For the recollapsing regions we find a family of (Kasner) attractors, so that generically these regions fall in spindlelike singularities. These results give substantial support to the idea that the Universe can be very inhomogeneous on ultralarge, superhorizon scales, with observers living in those (almost) isotropic regions that emerge from an inflationary phase.