Scalar Dark Matter with a non-elementary Higgs

In models with a scalar Dark Matter candidate, its interactions with the visible world are typically mediated by the Standard Model Higgs, i.e. through the so-called Higgs portal. However, if the physical Higgs particle is not exactly as predicted in the Standard Model, then the interactions of the scalar Dark Matter candidate are different from the traditional Higgs portal and new phenomenological signals are expected. In this talk, considering the framework with a non-elementary Higgs, the effective interactions of a Dark Matter candidate will be discussed, distinguishing two cases: the Dark Matter candidate is i) a real scalar field, or  ii) an axion-like-particle. The related phenomenology at colliders is illustrated.