Constraining the Nonextensive Mass Function of Halos from BAO, CMB and X-ray data

Clusters of galaxies are the most impressive gravitationally-bound systems in the Universe and its abundance (the cluster mass function) is one important statistics to probe the matter density parameter ($\Omega_m$) and the amplitude of density fluctuations ($\sigma_8$). The cluster mass function is usually described in terms of the Press-Schecther (PS) formalism where the primordial density fluctuations are assumed to be a Gaussian random field. In previous works we have proposed a non-Gaussian analytical extension of the PS approach with basis on the $q$-power law distribution (PL) of the non-extensive kinetic theory. In this paper, by applying the PL distribution to fit the observational mass function data from X-ray highest flux-limited sample (HIFLUGCS) we find a strong degeneracy among the cosmic parameters, $\sigma_8$, $\Omega_m$, and the $q$ parameter from the PL distribution. A joint analysis involving recent observations from baryon acoustic oscillation (BAO) peak and Cosmic Microwave Background (CMB) shift parameter is carried out in order to break these degeneracy and better constrain the physically relevant parameters. The present results suggest that the next generation of cluster surveys will be able to probe the quantities of cosmological interest ($\sigma_8, \Omega_m$) and the underlying cluster physics quantified by the $q$-parameter.