Beyond the Standard Model physics is required to explain both
dark matter and
the baryon asymmetry of the universe,
the latter possibly generated during a strong first-order electroweak phase transition.
While many proposed models tackle these problems
independently,
it is interesting to inquire whether the same model can explain both.
In this context,
we link state-of-the-art perturbative assessments of
the phase transition thermodynamics with
the extraction of the dark matter energy density.
These techniques are applied to
a next-to-minimal dark matter model containing
an inert
Majorana fermion that is coupled to
Standard Model leptons via
a scalar mediator,
where the mediator interacts directly with the Higgs boson.
For dark matter masses
180 GeV < M
χ ≲ 300 GeV,
we discern regions of the model parameter space that reproduce
the observed dark matter energy density and
allow for a first-order phase transition, while evading the most stringent collider constraints.