We study an extension of the Standard Model (SM) in which two copies of the SM scalar $SU(2)$ doublet which do not acquire a Vacuum Expectation Value (VEV), and hence are textit{inert}, are added to the scalar sector. We allow for CP-violation in the textit{inert} sector, where the lightest textit{inert} state is protected from decaying to SM particles through the conservation of a $Z_2$ symmetry. The lightest neutral particle from the textit{inert} sector, which has a mixed CP-charge due to CP-violation, is hence a Dark Matter (DM) candidate. We discuss the new regions of DM relic density opened up by CP-violation, and compare our results to the CP-conserving limit and the Inert Doublet Model (IDM). We constrain the parameter space of the CP-violating model using recent results from the Large Hadron Collider (LHC) and DM direct and indirect detection experiments.
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