The evolution of voids in the expanding universe

The growth and nonlinear evolution of spherically symmetric, negative density perturbations in an otherwise uniform Friedmann cosmology are examined, with attention to those cases in which the cavity comes to be surrounded by a narrow shell of matter whose density is substantially greater than the mean cosmological value. It is shown that such an overdense shell can form even when no overdense region is present in the initial density profile. It is suggested that such walled-in cavities may be identified with recently observed large scale holes in the galaxy distribution, while the shells themselves are identifiable with the superclusters defining the boundaries of such holes. Attention is also given to the behavior of the shell growth phenomenon under various background universe and initial density perturbation assumptions.