Linear Evolution of the Gravitational Potential: A New Approximation for the Nonlinear Evolution of Large-Scale Structure

Using a full nonlinear numerical gravitational clustering simulation with Ω = 1 cold dark matter and Zel'dovich initial conditions, we show that the gravitational potential evolves very little up to the present on length scales ≥ 1.25 h-1 Mpc. We present a new approximation for the nonlinear evolution of large-scale structure, in which the gravitational potential field is assumed to remain constant up to the present, but the matter obeys the usual nonlinear equations of motion in this potential field. We calculate evolved density fields using this approximation and compare them to the Zel'dovich approximation and a full nonlinear evolution. At late times, the accuracy of our results lies between the Zel'dovich approximation and a full nonlinear evolution.