Minimal self-interacting dark matter models with light mediator

The light mediator scenario of self-interacting dark matter is strongly constrained in many ways. After summarizing the various constraints, we discuss minimal options and models which allow to nevertheless satisfy all these constraints. One straightforward possibility arises if the dark matter and light mediator particles have a temperature sizably smaller than the SM particles. Another simple possibility arises if dark matter doesn't annihilate dominantly into a pair of light mediators but into heavier particles. Both possibilities are discussed with scalar as well as vector boson light mediators. Further possibilities, such as with a hierarchy of quartic scalar couplings, are also identified.