Demonstrating discreteness and collision error in cosmological N-body simulations of dark matter gravitational clustering

Two-body scattering and other discreteness effects are unimportant in cosmological gravitational clustering in most scenarios since the dark matter has a small particle mass. The collective field should determine evolution; two-body scattering in simulations violates the Poisson-Vlasov equations. We test this result in PM, (PM)-M-3, Tree, and NGPM codes, noting that a collisionless code will preserve the one-dimensional character of plane-wave collapse, We find collisionality vanishing as the softening parameter approaches the mean interparticle separation, Solutions for the problem are suggested, involving greater computer power, PM-based nested grid codes, and a more conservative approach to resolution claims.