Improvements in the M-T relation and mass function and the measured Omega_m through clusters evolution

In this paper, I revisit the constraints obtained by several authors (Reichart et al. 1999; Eke et al. 1998; Henry 2000) on the estimated values of Omega_m, n and sigma_8 in the light of recent theoretical developments: 1) new theoretical mass functions (Sheth & Tormen 1999, Sheth, Mo & Tormen 1999, Del Popolo 2002b); 2) a more accurate mass-temperature relation, also determined for arbitrary Omega_m and Omega_{\Lambda} (Voit 2000, Pierpaoli et al. 2001, Del Popolo 2002a). Firstly, using the quoted improvements, I re-derive an expression for the X-ray Luminosity Function (XLF), similarly to Reichart et al. (1999), and then I get some constraints to \Omega_m and n, by using the ROSAT BCS and EMSS samples and maximum-likelihood analysis. Then 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. Both in the case of the XLF and XTF, the changes in the mass function and M-T relation produces an increase in Omega_m of \simeq 20% and similar results in sigma_8 and n.