Measuring Omega(m) using clusters evolution

The constraints obtained by several authors (Eke et al. 1998; Henry 2000) on the estimated values of Omega(m), n and sigma(8) are revisited in the light of recent theoretical developments: 1) new theoretical mass functions; 2) a more accurate mass-temperature relation, also determined for arbitrary Omega(m) and Omega(Lambda). I re-derive the X-ray Temperature Function (XTF), similarly to Henry (2000) and Eke et al. (1999), re-obtaining the constraints on Omega(m), n, sigma(8). The result shows that changes in the mass function and M-T relation produces an increase in Omega(m) of similar or equal to20% and similar results in sigma(8) and n.