Dynamics of silent universes

We investigate the local nonlinear dynamics of irrotational dust with vanishing magnetic part of the Weyl tensor, H_ab. 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 H_ab = 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 Ω. 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 H_ab 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.