Scalar extensions of the SM and recent experimental anomalies

The Brout-Englert-Higgs mechanism describes the generation of masses of fundamental particles in the Standard Model (SM). It predicts the existence of one scalar particle with precisely predicted couplings to fermions and gauge bosons. Deviations from these predictions, such as the observation of additional scalar particles, would indicate non-minimal Higgs sectors and beyond-the-SM physics. We motivate extended scalar sectors based on theoretical and observational grounds and discuss their possible manifestations at colliders or gravitational-wave experiments. We explore smoking-gun signatures of electroweak baryogenesis at the LHC or a future $e^+e^-$ collider, and we examine their interplay with the observation of a primordial gravitational-wave background at LISA. We also consider the possibility of an additional Higgs boson at about 95 GeV motivated by excesses in diphoton and ditau final states observed by CMS. Finally, we discuss the impact of the CDF measurement of the $W$-boson mass on the parameter space of scalar extensions of the SM.