  The inert doublet dark matter model has recently gained attention as a
possible means of facilitating a strongly first order electroweak phase
transition (EWPT), as needed for baryogenesis. We extend previous results by
considering the regime where the DM is heavier than half the Higgs mass, and
its relic density is determined by annihilation into W, Z and Higgs bosons. We
find a large natural region of parameter space where the EWPT is strongly first
order, while the lightest inert doublet state typically contributes only 0.1-3%
of the total dark matter. Despite this small density, its interactions with
nucleons are strong enough to be directly detectable given a factor of 5
improvement over the current sensitivity of XENON100. A 10% decrease in the
branching ratio for Higgs decays to two photons is predicted.
