The stability of a collisionless cosmological shell

The P3 M technique is used here to simulate the evolution of collisionless shells in an Omega = 1 universe. Starting from the spherical similarity solution, a bootstrap technique is used to follow the evolution over very large expansion factors. It is found that the overall structure follows the similarity solution for a long period during which bound clumps grow within the shell. At late times the growth of structure depends on induced velocity perturbations in material outside the shell. If such perturbations are suppressed, structure on the shell becomes self-similar. When induced motions in the background medium are included, the evolution at late times is dominated by large-scale modes as predicted by linear stability analysis. The stable final state appears to consist of one or two massive clumps on the edge of a spherical void. The possible application of these results to the origin of galaxies and large-scale structure is discussed.