Linear scale bounds on dark matter--dark radiation interactions and connection with the small scale crisis of cold dark matter

One of the open questions in modern cosmology is the small scale crisis of the cold dark matter paradigm. Increasing attention has recently been devoted to self-interacting dark matter models as a possible answer. However, solving the so-called missing satellites problem requires in addition the presence of an extra relativistic particle (dubbed dark radiation) scattering with dark matter in the early universe. Here we investigate the impact of different theoretical models devising dark matter dark radiation interactions on large scale cosmological observables. We use cosmic microwave background data to put constraints on the dark radiation component and its coupling to dark matter. We find that the values of the coupling allowed by the data imply a cut-off scale of the halo mass function consistent with the one required to match the observations of satellites in the Milky Way.