The $\Lambda$CDM standard model of cosmology is in excellent
agreement with data on large scales but has difficulty explaining all
observations on small scales. I discuss a simple particle physics model
involving a new MeV-scale gauge boson that mediates dark matter
self-interactions and dark matter interactions with a new light fermion.
This allows to solve all small-scale problems of $\Lambda$CDM cosmology.
It would be very attractive to identify the new light particle with a
sterile neutrino, but it appears that this option is disfavored.