On local approximations to the nonlinear evolution of large-scale structure

We present a comparative analysis of several methods, known as local Lagran gian approximations, which are aimed to the description of the nonlinear ev olution of large-scale structure. We have investigated various aspects of t hese approximations, such as the evolution of a homogeneous ellipsoid, coll apse time as a function of initial conditions, and asymptotic behavior. As one of the common features of the local approximations, we found that the c alculated collapse time decreases asymptotically with the inverse of the in itial shear. Using these approximations, we have computed the cosmological mass function, finding reasonable agreement with N-body simulations and the Press-Schechter formula.