Non-linear evolution of the cosmological background density field as diagnostic of the cosmological reionization

We present constraints on the cosmological and reionization parameters based on the cumulative mass function of the Ly-α systems. We evaluate the formation rate of bound objects and their cumulative mass function for a class of flat cosmological models with cold dark matter plus cosmological constant or dark energy with constant equation of state encompassing different reionization scenarios and compare it with the cumulative mass function obtained from the Ly-α transmitted flux power spectrum. We find that the analysis of the cumulative mass function of the Ly-α systems indicates a reionization redshift zr = 24.2± 4 (68%CL) in agreement with the value found on the basis of the WMAP anisotropy measurements, setting constraints on the amplitude of the density contrast, σ8 = 0.91 ± 0.04 (68%CL), similar to those derived from the X-ray cluster temperature function. Our joint analysis of Ly-α cumulative mass function and WMAP anisotropy measurements shows that the possible current identification of a running of the slope, dns/dlnk 6= 0, at kp=0.05Mpc −1 (multipole l ≈ 700) is mainly an effect of the existing degeneracy in the amplitude-slope plane at this scale, the result being consistent with the absence of running, the other constraints based on WMAP data remaining substantially unchanged. Finally, we evaluate the progress on the determination the considered parameters achievable by using the final temperature anisotropy data from WMAP and from the forthcoming Planck satellite that will significantly improve the sensitivity and