Spherical Collapse Model And Dark Energy(II)

This is a second paper of a series of two. In this paper, we directly correct the problem pointed out in the first paper of this series, dark energy does not cluster on the scale of galaxy clusters, but the current describing the flowing of dark energy outside the clusters is ignored in almost all the previous papers. We derive a first order differential equation which describes the evolution of the clusters in a back ground universe containing dark energies. We solve this equation numerically and also provide a formal analytical solution for it. From the solution we extract the key parameters of the model and find them depending on the equation of state coefficients of dark energies rather non-trivially. We then use Press-Scheter theory and calculate the number density of galaxy clusters and its evolutions and find that they are both strongly affected by the equation of state coefficients of dark energies. Roughly speaking we find that if $-1<w<0$, the number density of galaxy clusters increases as we look back to the past. But if $w<-1$, the contrary is the case. Our conclusions in this paper are similar to those obtained in the companion paper of this one but rather different from the previous papers, which say that the equation of state coefficients of dark energies only affect the number density of galaxy clusters very weakly.