Gravitational Collapse in an Expanding Universe: Asymptotic Self-similar Solutions

The collapse and virialization of self-similar spherical density perturbations to a flat Einstein e Sitter universe is investigated and in particular the asymptotic similarity solutions. Previous calculations of Gunn and Fillmore & Goldreich of the asymptotic solutions are improved here and the collapse factor of a given spherical shell is calculated. Within the framework of the asymptotic behavior exact analytical solutions are obtained.