The growth of anisotropic structures in a Friedmann universe

The evolution of nonspherical structures was investigated when observational evidence for the existence of flattened or striated structures of about 100 Mpc was found. Equations describing the evolution of a rotating, dust ellipsoid in an expanding universe have been obtained, and solutions for the shape and density evolution as the ellipsoid expands with a Friedmann background universe have been derived. Details of pancake formation were calculated, and the density collapse at turnaround and the collapse velocity at pancake formation were found to be reduced relative to the spherical case when initial fluctuations were anisotropic. An exact model for a general relativistic pancake collapse has also been given, which is based on an exact solution to Einstein's equations and does not have symmetry or pass through a series of ellipsoids.