Cluster formation rate in models with dark energy

Based on flat Friedmann-Robertson-Walker cold dark matter (CDM) models driven by nonrelativistic matter and an exotic fluid (quintessence) with an equation of state p(Q) = wrho(Q) (-1 less than or equal to w < 0), we investigate whether or not the large-scale dynamical effects of cluster formation and virialization are related to the cosmic equation of state. Using nonlinear spherical collapse we find that the cluster formation rate in quintessence models is intermediate between open and ΛCDM. 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 turnaround radii. We find that the above ratio is almost independent of the equation of state.