The Nature of Dark Energy from deep Cluster Abundance

We show that using the redshift dependence of the deep cluster abundance to detect the nature of Dark Energy is a serious challenge. We compare the expected differences between flat LCDM models, with different Omega_mo, with the difference between LCDM and dynamical DE models. In the former case, cluster abundances in comoving volume and geometrical factors act in the same direction, yielding a significant difference between the expected angular densities. On the contrary, when we keep a constant Omega_mo and change the DE nature,abundances in comoving volume and geometrical factors act in the opposite direction, so that the expected differences in angular densities reduce to small factors.