A theory for expanding, large-scale, isolated, spherically-symmetric density perturbations with null peculiar velocity field

Exact theory for expanding density perturbations under the following assumptions: (1) Friedmann universes made of dust only; (2) spherically-symmetric perturbations; (3) isolated perturbations: and (4) null peculiar velocity field, is reviewed and extended. The overdensity equation is derived and the related solution is determined concerning both mean overdensity and local overdensity, and including both the growing and the decreasing mode, in terms of nondimensional variables normalized to the initial configuration. A first-order and zero-order approximation to the exact theory is also performed in view of applications to specific problems, e.g., the acquisition of angular momentum by tidal torques. The idealized case presented here makes a necessary reference in dealing with more general situations involving both analytical and numerical approaches.