Evolution of the potential in cosmological gravitational clustering

The gravitational potential is constant to linear order in cosmological gravitational clustering. In this paper we present results of testing the conjecture, proposed by Pauls & Melott, that the effect of nonlinear evolution on the potential can be better described by smoothing it on the scale of nonlinearity. We show two-dimensional simulations consisting of an N-body code in which particles are accelerated not by their mutual attraction, but by the gradient of the initial potential smoothed on the current scale of nonlinearity. This approximation produces results considerably improved over using a constant potential to move particles, and it is generally better than any scheme we have tested, lending further support to the smoothing description of the evolved potential. Subject headings: cosmology: theory - gravitation - large-scale structure of the universe -methods: numerical