Evolution of the luminosity function. In green, we show the prediction of our model when fitting for the LF itself at redshifts 0.25, 0.5, 3 and 6, as well as for the GW background measured by EPTA, displaying the median (green line) and 90% confidence interval (green band). This should be compared with the fits to the observed LF from Lacy et al. (2015) (pink) and Shen et al. (2020) (purple) and the region in between (light pink), where we allow the observed LF to lie in our likelihood. At redshifts z = 4, 5 we also plot constraints from JWST (squares) from Matthee et al. (2024). The lowest luminosity point is shown in grey and not in black, because it is likely affected by incompleteness (see the discussion in Matthee et al. 2024). At redshift z = 7, we plot a lower bound obtained by Greene et al. (2024) using JWST results.