Constraining the CDM spectrum normalization in flat dark energy cosmologies

We study the relation between the rms mass fluctuations on 8$h^{-1}$Mpc scales and $\Omega_{\rm m}$ using the recent clustering results of XMM-{\it Newton} soft (0.5-2 keV) X-ray sources, which have a median redshift of $z\sim 1.2$. The relation can be represented in the form $\sigma_{8}=0.34 (\pm 0.01) \Omega_{\rm m}^{-\gamma}$ where $\gamma\equiv \gamma(\Omega_{\rm m},w)$ and it is valid for all $w<-1/3$ models. By combining the X-ray clustering and SNIa data we find that the model which best reproduces the observational data is that with: $\Omega_{\rm m}\simeq 0.26$, $w\simeq -0.90$ and $\sigma_{8}\simeq 0.73$, which is in excellent agreement with the recent 3-year Wilkinson Microwave Anisotropy Probe results.