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The mass function of cluster-size halos and their redshift distribution arecomputed for 12 distinct accelerating cosmological scenarios and confronted tothe predictions of the conventional flat $\Lambda$CDM model. The comparisonwith $\Lambda$CDM is performed by a two-step process. Firstly, we determine thefree parameters of all models through a joint analysis involving the latestcosmological data, using SNe type Ia, the CMB shift parameter and BAO. Apartfrom a brane world inspired cosmology, it is found that the derived Hubblerelation of theremaining models reproduce the $\Lambda$CDM resultsapproximately with the same degree of statistical confidence. Secondly, inorder to attempt distinguish the different dark energy models from theexpectations of $\Lambda$CDM, we analyze the predicted cluster-size haloredshift distribution on the basis of two future cluster surveys: (i) an X-raysurvey based on the {\tt eROSITA} satellite, and (ii) a Sunayev-Zeldovichsurvey based on the South Pole Telescope. As a result, we find that thepredictions of 8 out of 12 dark energy models can be clearly distinguished fromthe $\Lambda$CDM cosmology, while the predictions of 4 models are statisticallyequivalent to those of the $\Lambda$CDM model, as far as the expected clustermass function and redshift distribution are concerned. The present analysissuggest that such a technique appears to be very competitive to independenttests probing the late time evolution of the Universe and the associated darkenergy effects.

Confronting Dark Energy Models using Galaxy Cluster Number Counts