Gravitational Evolution of a Perturbed Lattice and its Fluid Limit

We apply a simple linearization, well known in solid state physics, to approximate the evolution at earlytimes of cosmological N -body simulations of gravity. In the limit that the initial perturbations, applied toan infinite perfect lattice, are at wavelengths much greater than the lattice spacing l , the evolution isexactly that of a pressureless self-gravitating fluid treated in the analogous (Lagrangian) linearization,with the Zeldovich approximation as a subclass of asymptotic solutions. Our less restricted approximationallows one to trace the evolution of the discrete distribution until the time when particles approach oneanother (i.e., ''shell crossing''). We calculate modifications of the fluid evolution, explicitly dependent onl , i.e., discreteness effects in the N -body simulations. We note that these effects become increasinglyimportant as the initial redshift is increased at fixed l .