Constraining the Cold Dark Matter Spectrum Normalization in Flat Dark Energy Cosmologies

We study the relation between the rms mass fluctuations on 8 h^-1 Mpc scales and Ω_m using the recent clustering results of XMM-Newton soft (0.5-2 keV) X-ray sources, which have a median redshift of z~1.2. The relation can be represented in the form σ₈=0.34(+/-0.01)Ω^-γ_m, where γ≡γ(Ω_m, w), and it is valid for all w<-1/3 models. By combining the X-ray clustering and SN Ia data we find that the model that best reproduces the observational data is that with Ω_m~=0.26, w~=-0.90, and σ₈~=0.73, which is in excellent agreement with the recent 3 yr Wilkinson Microwave Anisotropy Probe results.