Expanding, homogeneous, ellipsoidal density perturbations. I - The effect of the initial shape at some special stages of evolution

The theory regarding expanding ellipsoidal density perturbations is extended to describe overdensity, unique evolutionary configurations, and their corresponding physical parameters. Theories by White and Silk (1979) and by More et al. (1986) regarding the expansion of homogeneous ellipsoidal density perturbations are reviewed. Attention is given to: (1) expressing the overdensity in terms of nondimensional variables; (2) describing flat and oblong configurations; and (3) conducting a deep analysis of the gravitational force induced on the unit mass at the top axes of the ellipsoid. Physical parameters are expressed for such effects as axis turn-around, maximum volume, or strong decoupling from the Hubble flow. Also described are the parameters for a range of initial shapes emphasizing inhomogeneities with galactic masses in a classical CDM scenario.