Ellipsoidal collapse and previrialization

We study the nonlinear evolution of a dust ellipsoid embedded in a flat Friedmann background universe, in order to determine the evolution of the density of the ellipsoid as the perturbation associated with it detaches from the general expansion and begins to collapse. We show that while the growth rate of the density contrast of a mass element is enhanced by shear, in agreement with Hoffman's 1986 result, the angular momentum acquired by the ellipsoid has the right magnitude to counterbalance the effect of the shear. This result confirms the previrialization conjecture by showing that initial asphericities and tidal interactions begin to slow the collapse after the system has broken away from the general expansion.