Evolution of the cluster mass function: Gpc(3) dark matter simulations

High-resolution N-body simulations of four popular cold dark matter cosmolo gies (LCDM, OCDM, QCDM, and tilted SCDM), each containing similar to 10(5) clusters of galaxies of mass M-1.5 > 5 x 10(13) h(-1) M. in a Gpc(3) volume , are used to determine the evolution of the cluster mass function from z = 3 to 0. The large volume and high resolution of these simulations allow an accurate measure of the evolution of cosmologically important (but rare) m assive clusters at high redshift. The simulated mass function is presented for cluster masses within several radii typically used observationally (R = 0.5, 1.0, and 1.5 h(-1) Mpc, both comoving and physical) in order to enabl e direct comparison with current and future observations. The simulated evo lution is compared with current observations of massive clusters at redshif ts 0.3 less than or similar to z less than or similar to 0.8. The Omega (m) = 1 tilted SCDM model, which exhibits very rapid evolution of the cluster abundance, dance, produces too few clusters at z greater than or similar to 0.3 and no massive clusters at z greater than or similar to 0.5 in stark c ontradiction to observations. The Omega (m) = 0.3 models-LCDM, OCDM, and QC DM-all exhibit considerably weaker evolution and are consistent with curren t data. Among these low-density models, OCDM evolves the least. These trend s are enhanced at high redshift and can be used to discriminate between fla t and open low-density models. The simulated mass functions are compared wi th the Press-Schechter approximation. Standard Press-Schechter predicts too many low-mass clusters at z = 0, and too few clusters at higher redshift. We modify the approximation by a simple parameterization of the density con trast threshold for collapse, which has a redshift dependence. This modifie d Press-Schechter approximation provides a good fit to the simulated mass f unctions.