Beyond the standard model via extended symmetries and dark matter

In this thesis, we discuss ideas of how to go beyond the Standard Model (SM) of particle physics to incorporate the cosmological observations of dark matter and matter–antimatter asymmetry, and to address the theoretical problems related to the scalar sector of the SM. Although the SM has proven to be an excellent description of the interactions of elementary particles, there is both experimental and theoretical evidence that this description cannot be complete. Most notably, the cosmological observations of dark matter (DM) and the matter–antimatter asymmetry in the universe cannot be explained within the SM. We have studied simple singlet extensions of the SM. We found out that these DM and matter–antimatter-asymmetry problems cannot be solved simultaneously by adding only one real singlet scalar, but already a singlet sector consisting of the scalar and an additional fermionic DM candidate is sufficient. This study also lays the ground for more complex extensions. Further, we found out that already one additional scalar can help stabilising the SM vacuum. Another hint beyond the SM is the vast hierarchy between the mass of the Higgs boson and the Planck scale, the natural cut-off of the SM. The naturalness problem associated with light elementary scalars motivates the study of a dynamical origin behind the electroweak symmetry breaking. Whereas an underlying strongly coupled sector can explain the hierarchy between the electroweak and the Planck scales dynamically, there is no simple way to give masses for the SM fermions without scalars. An alternative route is to combine the dynamical electroweak symmetry breaking and elementary scalars responsible for fermion masses. This is motivated by a possibility of high-energy completion of this class of models via e.g. supersymmetry or a non-trivial ultraviolet fixed point for the couplings. We have studied a specific model of this kind in the light of current data from the LHC run I and found the model viable. The light SM Higgs boson might also imply a symmetry protecting the mass of the scalar. We have pursued this idea by extending the global symmetry of the SM scalar sector to SU(4) and studied the spontaneous breaking of this global symmetry to Sp(4). We found that with elementary scalars, the SM interactions breaking this global symmetry naturally prefer the Goldstone-boson nature of the Higgs boson. Further, there is a remaining pseudo-Goldstone boson that can act as a viable DM candidate producing the observed relic abundance while escaping the current stringent experimental bounds for DM detection.