Cluster Formation Rate in Models with Dark Energy

Based on flat Friedmann-Robertson Walker cold dark matter (CDM) type modelsdriven by non-relativistic matter and an exotic fluid (quintessence) with anequation of state: $p_{Q}=w\rho_{Q}$ ($-1\le w<0$), we investigate whether ornot the large scale dynamical effects regarding the cluster formation andvirialization are related to the cosmic equation of state. Using the non-linearspherical collapse we find that the cluster formation rate, in quintessencemodels, is intermediate between the open and $\Lambda$CDM respectively. For theQCDM case, using the virial theorem and energy conservation and assuming aspherical mass overdensity shell, we obtain analytically the ratio between thefinal (virial) and the turn-around radius. We find that the above ratio isalmost independent from the equation of state.Comment: 13 pages, including 3 figures, accepted for publication in ApJ Vol: 590, June 2003. Minor change