  The cold dark matter (CDM) model faces persistent challenges on small scales.
In particular, taken at face value, the model significantly overestimates the
number of satellite galaxies around the Milky Way. Attempts to solve this
problem remain open to debate and have even led some to abandon CDM altogether.
However, current simulations are limited by the assumption that dark matter
feels only gravity. Here, we show that including interactions between CDM and
radiation (photons or neutrinos) leads to a dramatic reduction in the number of
satellite galaxies, alleviating the Milky Way satellite problem and indicating
that physics beyond gravity may be essential to make accurate predictions of
structure formation on small scales. The methodology introduced here gives
constraints on dark matter interactions that are significantly improved over
those from the cosmic microwave background.
