Making use of a dimensionally-reduced effective theory at high temperature, we perform a nonperturbative study of the electroweak phase transition in the Two Higgs Doublet model. We focus on two phenomenologically allowed points in the parameter space, carrying out dynamical lattice simulations to determine the equilibrium properties of the transition. We discuss the shortcomings of conventional perturbative approaches based on the resummed effective potential — regarding the insufficient handling of infrared resummation but also the need to account for corrections beyond 1-loop order in the presence of large scalar couplings — and demonstrate that greater accuracy can be achieved with perturbative methods within the effective theory. We find that in the presence of very large scalar couplings, strong phase transitions cannot be reliably studied with any of the methods.

We catalogue and study three-Higgs-doublet models in terms of all possible allowed symmetries (continuous and discrete, Abelian and non-Abelian), where such symmetries may be identified as flavour symmetries of quarks and leptons. We analyse the potential in each case, and derive the conditions under which the vacuum alignments (0, 0, v), (0, v, v) and (v, v, v) are minima of the potential. For the alignment (0, 0, v), relevant for dark matter models, we calculate the corresponding physical Higgs boson mass spectrum. Motivated by supersymmetry, we extend the analysis to the case of three up-type Higgs doublets and three down-type Higgs doublets (six doublets in total). Many of the results are also applicable to flavon models where the three Higgs doublets are replaced by three electroweak singlets.

In many models, stability of dark-matter particles is protected by a conserved Z2 quantum number. However, dark matter can be stabilized by other discrete symmetry groups, and examples of such models with custom-tailored field content have been proposed. Here, we show that electroweak symmetry-breaking models with N Higgs doublets can readily accommodate scalar dark matter candidates stabilized by groups Zp with any p$\le${}2N-1, leading to a variety of kinds of microscopic dynamics in the dark sector. We give examples in which semiannihilation or multiple semiannihilation processes are allowed or forbidden, which can be especially interesting in the case of asymmetric dark matter.