The standard cosmological model based on cold dark matter (CDM) predicts a large number of subhalos for each galaxy-size halo. Matching the subhalos to the observed properties of luminous satellites of galaxies in the local universe poses a significant challenge to our understanding of the astrophysics of galaxy formation. We show that the cosmic evolution and host mass dependence of the luminosity function of satellites provide a powerful new diagnostic to disentangle astrophysical effects from variations in the underlying dark matter mass function. We illustrate this by comparing recent observations of satellites between redshifts 0.1 z 0.8 based on Hubble Space Telescope images, with predictions from three different state-of-the-art semi-analytic models applied to CDM power spectra, with one model also applied to a warm dark matter (WDM) spectrum. We find that even though CDM models provide a reasonable fit to the local luminosity function of satellites around galaxies comparable to the Milky Way, they do not reproduce the data as well for different redshifts and host galaxy stellar masses, indicating that further improvements in the description of star formation are likely needed. The WDM model matches the observed mass dependence and redshift evolution of satellite galaxies more closely, indicating that a modification of the underlying power spectrum may offer an alternative solution to this tension. We conclude by presenting predictions for the color distribution of satellite galaxies to demonstrate how future observations will be able to further distinguish between these models and to help constrain baryonic and non-baryonic physics.
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