  Interactions between dark matter (DM) and radiation (photons or neutrinos) in
the early Universe suppress density fluctuations on small mass scales. Here we
perform a thorough analysis of structure formation in the fully non-linear
regime using N-body simulations for models with DM-radiation interactions and
compare the results to a traditional calculation in which DM only interacts
gravitationally. Significant differences arise due to the presence of
interactions, in terms of the number of low-mass DM haloes and their
properties, such as their spin and density profile. These differences are
clearly seen even for haloes more massive than the scale on which density
fluctuations are suppressed. We also show that semi-analytical descriptions of
the matter distribution in the non-linear regime fail to reproduce our
numerical results, emphasizing the challenge of predicting structure formation
in models with physics beyond collisionless DM.
