Understanding the Cosmic Mass Function High-Mass Behavior

We claim that the discrepancy found between the theoretical predictions for the cosmic mass function and those found in numerical simulations is due to the fact that in deriving the former, all mass elements are assumed to be at the center of the object they belong to (the all-mass-at-center problem). By an appropriate treatment of this problem, using the spherical collapse model (which is not a bad approximation in the high-mass limit), we obtain both the high-mass behavior found in simulations and the true asymptotic behavior of the mass function (for arbitrarily high masses). Therefore, we conclude that, by combining ellipsoidal dynamics with a suitable treatment of the all-mass-at-center problem (which we will show in follow-up work), a theoretical prediction for the cosmic mass function in full agreement with simulations may be obtained.