Demonstrating Discreteness and Collision Error in Cosmological [ITAL]N[/ITAL]-Body Simulations of Dark Matter Gravitational Clustering

Two-body scattering and other discreteness effects are unimportant incosmological gravitational clustering in most scenarios, since the dark matterhas a small particle mass. The collective field should determine evolution:Two-body scattering in simulations violates the Poisson-Vlasov equations. Wetest this in PM, P$^3$M, Tree, and NGPM codes, noting that a collisionless codewill preserve the one-dimensional character of plane wave collapse. We findcollisionality vanishing as the softening parameter approaches the meaninterparticle separation. Solutions for the problem are suggested, involvinggreater computer power, PM-based nested grid codes, and a more conservativeapproach to resolution claims.Comment: Final version accepted for ApJ Letters. Minor revisions, including due to bug fix in tree code. Uses aasms4.sty. 15 pages. Higher resolution figures available at ftp://kusmos.phsx.ukans.edu/preprints/discret