Confronting dark energy models using galaxy cluster number counts

The mass function of cluster-size halos and their redshift distribution are computed for 12 distinct accelerating cosmological scenarios and confronted to the predictions of the conventional flat $\Lambda \mathrm{CDM}$ model. The comparison with $\Lambda \mathrm{CDM}$ is performed by a two-step process. First, we determine the free parameters of all models through a joint analysis involving the latest cosmological data, using supernovae type Ia, the cosmic microwave background shift parameter, and baryon acoustic oscillations. Apart from a braneworld inspired cosmology, it is found that the derived Hubble relation of the remaining models reproduces the $\Lambda \mathrm{CDM}$ results approximately with the same degree of statistical confidence. Second, in order to attempt to distinguish the different dark energy models from the expectations of $\Lambda \mathrm{CDM}$, we analyze the predicted cluster-size halo redshift distribution on the basis of two future cluster surveys: (i) an X-ray survey based on the eROSITA satellite, and (ii) a Sunayev-Zeldovich survey based on the South Pole Telescope. As a result, we find that the predictions of 8 out of 12 dark energy models can be clearly distinguished from the $\Lambda \mathrm{CDM}$ cosmology, while the predictions of 4 models are statistically equivalent to those of the $\Lambda \mathrm{CDM}$ model, as far as the expected cluster mass function and redshift distribution are concerned. The present analysis suggests that such a technique appears to be very competitive to independent tests probing the late time evolution of the Universe and the associated dark energy effects.

Figure 1

The halo mass function at two different redshifts. The different DE models are represented by different symbols and/or line types (see Table  for definitions).

Figure 2

The expected redshift distribution of $M\gtrsim {10}^{14}{M}_{\odot }$ clusters (upper panel) of the different DE models and the corresponding fractional difference between the models and the reference $\Lambda \mathrm{CDM}$ model (lower panel). The lower panel shows only those DE models that have fractional relative differences, with respect to the $\Lambda \mathrm{CDM}$ model, of $\lesssim 45\%$. Symbols correspond to the different DE models as indicated in Table .

Figure 3

The expected cluster redshift distribution of the different DE models and for the two different future cluster surveys (upper panels), and the corresponding fractional difference with respect to the reference $\Lambda \mathrm{CDM}$ model (lower panels). Symbols correspond to the different DE models as indicated in Table .