Evolution of various plasma quantities as a function of redshift and for different values of z_max. Each curve represents the average value of the quantity over N_tree = 10³ merger trees (see Appendix C) for which a redshift-dependent, one-dimensional profile has been calculated according to Eqs. (19) and (21). The age of the Universe t_U at each redshift is plotted on the second x-axis. In order to assess the validity of our model, we added observed values for the temperature and the thermal electron density (see the detailed list in the main text).