Example of six different CR electrons spectra computed by our post-processing model, for different (random) variations of the combinations between gas density, magnetic field strength, redshift, and time elapsed since the injection of the initial power-law distribution of CRs. Such spectra are extracted from our tabulated list of spectra generated with the ROGER code and applied to compute the synchrotron emission from every cell in our simulated volumes in post-processing. Finally, we note that our approach neglects the spatial diffusion of cosmic rays, which is mostly negligible on the scales of interest here (this is addressed in more detail in Sect. 4).