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 quantify the systematic errors and the statistical uncertainties on the estimate 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 scatter around the relation between cluster X-ray luminosity and temperature to 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 relatively large uncertainties on this estimate of Omega (0), of the order of Delta (stat)Omega (0) = 0.1 at the 1 sigma level. On the other hand, the statistical 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 understanding of the cluster observed properties both in the local Universe and at high redshift, that is the relation between cluster mass, temperature and luminosity. This requires detailed observations of X-ray selected cluster samples, in comparison with hydrodynamic simulations including refined physics.