Dynamics of Silent Universes

We investigate the local nonlinear dynamics of irrotational dust with vanishing magnetic part of the Weyl tensor, Hab. Once coded in the initial conditions, this dynamical restriction is respected by the relativistic evolution equations. Thus, the outcome of the latter are exact solutions for special initial conditions with Hab = 0, but with no symmetries: they describe inhomogeneous triaxial dynamics generalizing that for a fluid element in a Tolman-Bondi, Kantowski-Sachs, or Szekeres geometry. A subset of these solutions may be seen as (special) perturbations of Friedmann models, in the sense that there are trajectories in phase-space that pass arbitrarily close to the isotropic ones. We find that the final fate of ever-expanding configurations is a spherical void, locally corresponding to a Milne universe. For collapsing configurations we find a whole family of triaxial attractors, with vanishing local density parameter Omega. These attractors locally correspond to Kasner vacuum solutions: only a set of measure zero of physical configurations collapses to a degenerate pancake, while the generic configuration collapses to a triaxial spindle singularity. These silent universe models may provide a fair representation of the universe on superhorizon scales. Moreover, one might conjecture that the nonlocal information carried by Hab becomes negligible during the late highly nonlinear stages of collapse, so that the attractors we find may be all those relevant for expanding or collapsing configurations of irrotational dust