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-alpha systems. We find that the analysis of the cumulative mass function of the Ly-alpha systems indicates a reionization redshift z_r=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, sigma_8=0.91+-0.04 (68\CL), similar to those derived from the X-ray cluster temperature function. Our joint analysis of Ly-alpha cumulative mass function and WMAP anisotropy measurements shows that the possible current identification of a running of the slope, dn_s/dlnk \ne 0, at k_p=0.05Mpc^-1 (multipole l of about 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 reliability of these results. This work has been done in the framework of the Planck LFI activities.