Consistency of a gauged two-Higgs-doublet model: Scalar sector

We study the theoretical and phenomenological constraints imposed on the scalar sector of the gauged two Higgs doublet model proposed recently as a variant of the popular inert Higgs doublet model of dark matter. The requirements of tree-level vacuum stability and perturbative unitarity in the scalar sector are analyzed in detail. Furthermore, taking into account the constraints from the 125 GeV Higgs boson measurements at the Large Hadron Collider, we map out the allowed ranges for the fundamental parameters of the scalar potential in the model.