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)A. 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 (asymptotically equal) 20% and similar results in (sigma)8 and n.