Precollapse scale invariance in gravitational instability

The transition to the very nonlinear regime during the gravitational collapse of collisionless matter in an Omega = 1 expanding universe is numerically and analytically investigated. Numerical simulations with very different initial conditions are used to show that a power-law density profile establishes progressively until the collapse time. A general method to obtain analytical approximations of higher order than those of Zeldovich for any type of initial perturbation is described. This formalism, explicitly applied in one particular case, confirms the numerical findings. The reliability of the numerical results and the importance of precollapse scale-invariance as a complement of previous works on self-similar properties of gravitational collapse are discussed.