CONSTRAINTS ON DARK ENERGY FROM THE ABUNDANCE OF GALAXY CLUSTERS: EFFECTS OF REDSHIFT UNCERTAINTIES AND MASS THRESHOLD

In the coming years, the next generation wide field surveys will lead to the discovery of large numbers of galaxy clusters, both from optical identifications and through the Sunyev-Zel’dovich effect, providing extensive databases to study these objects. The abundance of clusters above a given mass threshold as a function of redshift is sensitive to the Dark Energy (DE) equation of state (eos) and, therefore, this observable can be used to constrain its parameters. In this work we assume the simple eos p = wρ and study the impact of the mass threshold and the width of the redshift bin on the determination w. We use a Monte Carlo approach generating many realizations of the cluster distribution with a fiducial value of the eos parameter and obtaining the best fitting value of w and its uncertainty. We use two methods to recover w: the standard X² for the number of clusters in each bin and a product of Poisson distributions for each bin. Our results show that the uncertainty in w is independent of the redshift bin width and strongly dependent on the mass threshold. For both methods, the correct values of w are recovered when the mass threshold is smaller than ~ 10¹⁵h⁻¹ M_⊙. However, for higher masses, the X² method introduces a significant bias in w.