Cold dark matter variant cosmological models - I. Simulations and preliminary comparisons

We present two matched sets of five dissipationless simulations each, including four presently favoured minimal modifications to the standard cold dark matter (CDM) scenario. One simulation suite, with a linear box size of 75h^-1Mpc, is designed for high resolution and good statistics on the group/poor cluster scale, and the other, with a box size of 300h^-1Mpc, is designed for good rich cluster statistics. All runs had 57 million cold particles, and models with massive neutrinos (CHDM-2nu) had an additional 113 million hot particles. We consider separately models with massive neutrinos, tilt, curvature, and a non-zero cosmological constant (Lambda=3H^2_0Omega_Lambda) in addition to the standard CDM model. We find that the dark matter in each of our tilted Omega_0+Omega_Lambda=1 (TLambdaCDM) model with Omega_0=0.4, our tilted Omega_01 model (TCDM), and our open Lambda=0 (OCDM) model with Omega=0.5 has too much small-scale power by a factor of ~2, while CHDM-2nu and SCDM are acceptable fits. In addition, we take advantage of the large dynamic range in detectable halo masses afforded by the combination of the two sets of simulations to test the Press-Schechter approximation. We find good fits at cluster masses for delta_c,g=1.27-1.35 for a Gaussian filter and delta_c,t=1.57-1.73 for a top hat filter. However, when we adjust delta_c to obtain a good fit at cluster mass scales, we find that the Press-Schechter model overpredicts the number density of haloes compared to the simulations by a weakly cosmology-dependent factor of 1.5-2 at galaxy and group masses. It is impossible to obtain a good fit over the entire range of masses simulated by adjusting delta_c within reasonable bounds.