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Inert scalars and vacuum metastability around the electroweak scale

We analyse effective potential around the electroweak (EW) scale in the Standard Model extended with a heavy scalar doublet. We show that the additional scalars can have a strong impact on vacuum stability. Although the additional heavy scalars may improve the behaviour of running Higgs self-coupling at large field values, we prove that they can destabilise the vacuum due to EW-scale effects. A new EW symmetry conserving minimum of the effective potential can appear rendering the electroweak symmetry breaking minimum meta- or unstable. However, for the case of the inert doublet model (IDM) with a 125 GeV Higgs boson we demonstrate that the parameter space region where the vacuum is meta- or unstable cannot be reconciled with the constraints from perturbative unitarity, electroweak precision tests and dark matter relic abundance measurements.