Improvements in the M-T relation, mass function, and measured value of Omega(m) through cluster evolution

In this paper I revisit the constraints obtained by several authors on the estimated values of Omega(m), n, and sigma(8) in light of recent theoretical developments: (1) new theoretical mass functions and (2) a more accurate mass-temperature relation, also determined for arbitrary Omega(m) and Omega(Lambda). First, using the quoted improvements, I rederive an expression for the X-ray luminosity function (XLF) similarly to Reichart and coworkers, and then I obtain constraints on Omega(m) and n by using the ROSAT Brightest Cluster Sample, an Einstein Extended Medium-Sensitivity Survey sample, and maximum likelihood analysis. Then I rederive the X-ray temperature function (XTF) similarly to Henry and to Eke and coworkers, reobtaining the constraints on Omega(m), n, sigma(8). In the cases of both the XLF and XTF, the changes in the mass function and M-T relation produce an increase in Omega(m) of similar or equal to20% and similar results in sigma(8) and n.