The cold dark matter paradigm describes the large-scale structure of the Universe remarkably well. However, there exists some tension with the observed abundances and internal density structures of both field dwarf galaxies and galactic satellites. Here, we demonstrate that a simple class of dark matter models may offer a viable solution to all of these problems simultaneously. Their key phenomenological properties are velocity-dependent self-interactions mediated by a light vector messenger and thermal production with much later kinetic decoupling than in the standard case.

We consider dark matter consisting of weakly interacting massive particles (WIMPs) and revisit in detail its thermal evolution in the early universe, with a particular focus on models where the annihilation rate is enhanced by the Sommerfeld effect. After chemical decoupling, or freeze-out, dark matter no longer annihilates but is still kept in local thermal equilibrium due to scattering events with the much more abundant standard model particles. During kinetic decoupling, even these processes stop to be effective, which eventually sets the scale for a small-scale cutoff in the matter density fluctuations. Afterwards, the WIMP temperature decreases more quickly than the heat bath temperature, which causes dark matter to reenter an era of annihilation if the cross-section is enhanced by the Sommerfeld effect. Here, we give a detailed and self-consistent description of these effects. As an application, we consider the phenomenology of simple leptophilic models that have been discussed in the literature and find that the relic abundance can be affected by as much two orders of magnitude or more. We also compute the mass of the smallest dark matter subhalos in these models and find it to be in the range O(10 −10 M ) − O(10 M ); even much larger cutoff values are possible if the WIMPs couple to force carriers lighter than about 100 MeV. We point out that a precise determination of the cutoff mass allows to infer new limits on the model parameters, in particular from gamma-ray observations of galaxy clusters, that are highly complementary to existing constraints from g − 2 or beam dump experiments.PACS numbers: 95.35.+d, 98.80.Cq, 95.30.Tg