Cluster Formation Rate in Models with Dark Energy

Based on flat Friedmann-Robertson Walker cold dark matter (CDM) type models driven by non-relativistic matter and an exotic fluid (quintessence) with an equation of state: $p_Q=w{\rho }_Q$ ($-1\le w<0$), we investigate whether or not the large scale dynamical effects regarding the cluster formation and virialization are related to the cosmic equation of state. Using the non-linear spherical collapse we find that the cluster formation rate, in quintessence models, is intermediate between the open and $\mathrm{\Lambda }$CDM respectively. For the QCDM case, using the virial theorem and energy conservation and assuming a spherical mass overdensity shell, we obtain analytically the ratio between the final (virial) and the turn-around radius. We find that the above ratio is almost independent from the equation of state.