Constraining cosmological parameters with the clustering properties of galaxy clusters in optical and X-ray bands

Abstract

(abridged) We use a theoretical model to predict the clustering properties of galaxy clusters. Our technique accounts for past light-cone effects on the observed clustering and follows the non-linear evolution of the dark matter correlation function and cluster bias factor. A linear treatment of redshift-space distortions is also included. We perform a maximum-likelihood analysis by comparing the theoretical predictions to a set of observational data, both in the optical (APM and EDCC catalogues) and X-ray band (RASS1 Bright Sample, BCS, XBACs, REFLEX). In the framework of CDM models, we compute the constraints on cosmological parameters. Our results show that X-ray data are more powerful than optical ones, allowing smaller regions in the parameter space. We find that the clustering properties of clusters are almost independent of the matter density parameter and of the presence of a cosmological constant, while they appear to be strongly dependent on the shape parameter. Using the X-ray data only, we obtain Gamma~0.1 and 0.4<sigma_8<1.1 for the Einstein-de Sitter model, while 0.14<Gamma<0.22 and 0.6<sigma_8<1.3 for open and flat models with Omega_0m=0.3. Finally, we use our model to make predictions on the correlation length of galaxy clusters expected in future surveys. In particular, we show the results for an optical catalogue with characteristics similar to the EIS project and for a very deep X-ray catalogue with the characteristics of the XMM/LSS survey. We find that clusters at high redshifts are expected to have larger a correlation length than local ones.