Constraints to cosmological parameters 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 Ωm, n and σ8 in the light of recent theoretical developments: 1) new theoretical mass functions (Sheth & Tormen 1999, Sheth, Mo & Tormen 2001, Del Popolo 2002b); 2) a more accurate mass-temperature relation, also determined for arbitrary Ωm and ΩΛ (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 Ωm 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), re-obtaining the constraints on Ωm, n, σ8. Both in the case of the XLF and XTF, the changes in the mass function and M-T relation produces an increase in Ωm of ≃ 20% and similar results in σ8 and n.