CP violation and BSM Higgs bosons

We study extensions of the Standard Model (SM) in which copies of the SM scalar SU(2) doublet are added to the Higgs sector. These scalar doublets either acquire a Vacuum Expectation Value (VEV) and hence are active or do not develop a VEV and are inert. We consider CP-violation (CPV) in both the active and inert sector. As an example of a model with CPV in the active sector, we present a Type-I 2-Higgs-Doublet Model (2HDM) with two active doublets and show Large Hadron Collider (LHC) signals of such a scenario. The amount of CPV in this case is very limited due to constraints coming from Electric Dipole Moment experiments. Moreover, 2HDMs with only active doublets do not provide a Dark Matter (DM) candidate. As a result, we turn to 3-Higgs-Doublet Models (3HDMs) where unbounded CPV and viable DM candidates could be introduced simultaneously in the inert sector. We investigate DM phenomenology of such models.