Formation and Evolution of
Galaxy Clusters Across Cosmic Time

We study the r-band luminosity function (LF) of galaxies in clusters and their environment, its mass dependence and evolution over cosmic time up to z=2.8. We post-processed data from the C-EAGLE simulation project, formed by 30 high-resolution simulations of galaxy clusters, computing galaxy luminosities in different bands from UV to IR, using the E-MILES stellar spectra library. The (stacked) LFs inside r200 are already well defined at z=2.8. Overall, the LFs faint-end shows relatively little time evolution and a modest dependence on the cluster mass. The clusters are rich in dwarf galaxies at all times, with their LF's faint-end constantly steeper than alpha=-1.28 +/- 0.04, although it does not reach the halo mass function slope. Remarkably, all the clusters develop a faint-end upturn at z < 0.35, best modelled with a double Schechter function, with the clusters having log(M200/Msun)