N-point correlations in CDM and ΩCDM simulations

Higher order statistics are investigated in Omega cold dark matter (CDM) universes by analyzing 500 h(-1) Mpc high-resolution tree N-body simulations with both Omega = 1 and Omega < 1. The amplitudes of the N-point correlation functions are calculated from moments of counts-in-cells determined by a pair of new algorithms especially developed for large simulations. This approach enables massive oversampling with similar or equal to 10(9)-10(14) cells for accurate determination of factorial moments from up to 47 million particles in the scale range of 8 h(-1) kpc-125 h(-1) Mpc. Thorough investigation shows that there are three scale ranges in the simulations: greater than or equal to 8 h(-1) Mpc, a weakly nonlinear regime where perturbation theory applies with utmost precision; 1-8 h(-1) Mpc, the nonlinear plateau; and finally less than or equal to 1 h(-1) Mpc, a regime where dynamical discreteness effects dominate the higher order statistics. In the physically relevant range of 1-125 h(-1) Mpc the results (1) confirm the validity of perturbation theory in the weakly nonlinear regime; (2) establish the existence of a plateau in the highly nonlinear regime similar to the one observed in scale-free simulations; (3) show extended perturbation theory to be an excellent approximation for the nonlinear regime; (4) find the time-dependence of the S-N's to be negligible in both regimes; (5) in comparison with similar measurements in the Edinburgh-Durham Southern Galaxy Catalog survey, strongly support Omega < 1 with no biasing; and (6) show that the formulae of Szapudi and Colombi provide a good approximation for errors on higher order statistics measured in N-body simulations.