  Recently we studied the direct detection of multi-component dark matter with
arbitrary local energy densities. Although the generation of the dark matter
relic abundance is model-dependent, and in principle could be only indirectly
related to direct detection, it is interesting to consider the implications of
the former on the latter. In this work we conduct an extended analysis to
include constraints from two natural scenarios of dark matter genesis:
asymmetric dark matter and thermal freeze-out. In the first (second) case, the
dark matter number (energy) densities of the different components are expected
to be similar. In the case of thermal freeze-out, we assume that the global
energy density scales with the local one. In our numerical analysis we analyse
the median sensitivity of direct detection experiments to discriminate a
two-component scenario from a one-component one, and also the precision with
which dark matter parameters can be extracted. We analyse these generic
scenarios for both light and heavy mediators. We find that most scenarios have
a relatively suppressed maximum median sensitivity compared to the previously
studied general cases. We also find that the asymmetric scenario is more
promising than the thermal freeze-out one.
