  Warm dark matter cosmologies have been widely studied as an alternative to
the cold dark matter paradigm, the characteristic feature being a suppression
of structure formation on small cosmological scales. A very similar situation
occurs if standard cold dark matter particles are kept in local thermal
equilibrium with a, possibly dark, relativistic species until the universe has
cooled down to keV temperatures. We perform a systematic phenomenological study
of this possibility, and classify all minimal models containing dark matter and
an arbitrary radiation component that allow such a late kinetic decoupling. We
recover explicit cases recently discussed in the literature and identify new
classes of examples that are very interesting from a model-building point of
view. In some of these models dark matter is inevitably self-interacting, which
is remarkable in view of recent observational support for this possibility.
Hence, dark matter models featuring late kinetic decoupling have the potential
not only to alleviate the missing satellites problem but also to address other
problems of the cosmological concordance model on small scales, in particular
the cusp-core and too-big-too-fail problems, in some cases without invoking any
additional input.
