Thermal decoupling and the smallest subhalo mass in dark matter models
  with Sommerfeld-enhanced annihilation rates
  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 of
about 10^{-10} to 10 solar masses; 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.
