On the errors on Omega(0): Monte Carlo simulations of the EMSS cluster sample

We perform Monte Carlo simulations of synthetic EMSS cluster samples, to qu antify the systematic errors and the statistical uncertainties on the estim ate of Omega (0) derived from fits to the cluster number density evolution and to the X-ray temperature distribution up to z=0.83. We identify the sca tter around the relation between cluster X-ray luminosity and temperature t o be a source of systematic error, of the order of Delta (syst)Omega (0) = 0.09, if not properly taken into account in the modelling. After correcting for this bias, our best Omega (0) is 0.66. The uncertainties on the shape and normalization of the power spectrum of matter fluctuations imply relati vely large uncertainties on this estimate of Omega (0), of the order of Del ta (stat)Omega (0) = 0.1 at the 1 sigma level. On the other hand, the stati stical uncertainties due to the finite size of the high-redshift sample are twice as small. Therefore, what is needed in order to improve the accuracy of Omega (0) estimates based on cluster number density evolution is a more reliable measure of the local temperature function and a better understand ing of the cluster observed properties both in the local Universe and at hi gh redshift, that is the relation between cluster mass, temperature and lum inosity. This requires detailed observations of X-ray selected cluster samp les, in comparison with hydrodynamic simulations including refined physics.