Nonlinear Evolution of Density Perturbations

: From the epoch of recombination $(z\approx {10}^3)$ till today, the typical density contrasts have grown by a factor of about ${10}^6$ in a Friedmann universe with $\mathrm{\Omega }=1$. However, during the same epoch the typical gravitational potential has grown only by a factor of order unity. We present theoretical arguments explaining the origin of this approximate constancy of gravitational potential. This fact can be exploited to provide a new, powerful, approximation scheme to study the formation of nonlinear structures in the universe. The essential idea of this method is to evolve the initial distribution of particles using a gravitational potential frozen in time (Frozen Potential Approximation). This approximation provides valuable insight into understanding various features of nonlinear evolution; for example, it provides a simple explanation as to why pancakes remain thin during the evolution even in the absence of any artificial, adhesion-like, damping terms. We compare the trajectories of particles in various approximations. We also discuss a few applications of the frozen potential approximation.