  The complex scalar dark matter (DM) candidate in the gauged two Higgs doublet
model (G2HDM), stabilized by a peculiar hidden parity ($h$-parity), is studied
in detail. We explore the parameter space for the DM candidate by taking into
account the most recent DM constraints from various experiments, in particular,
the PLANCK relic density measurement and the current DM direct detection limit
from XENON1T. We separate our analysis in three possible compositions for the
mixing of the complex scalar. We first constrain our parameter space with the
vacuum stability and perturbative unitarity conditions for the scalar
potential, LHC Higgs measurements, plus Drell-Yan and electroweak precision
test constraints on the gauge sector. We find that DM dominated by composition
of the inert doublet scalar is completely excluded by further combining the
previous constraints with both the latest results from PLANCK and XENON1T. We
also demonstrate that the remaining parameter space with two other DM
compositions can be further tested by indirect detection like the future CTA
gamma-ray telescope.
