New Physics Ideas from Strongly Coupled Theories

The work in this thesis attempts to account for New Physics (NP) to extend the Standard Model (SM) in two complementary ways. The main aim is to address the problem of dark sectors/dark matter in the SM. The first part of the thesis extends the SM with a putative new sector which is SM-neutral and light with mass similar to the MeV scale. This dark sector can give phenomenological signatures in future neutrino oscillation experiments. The second part of the thesis involves extending both the SM matter and SM gauge group with a new strong force called dark colour. Vector-like dark fermions charged under dark colour are added which can give a composite baryon - a dark matter candidate with mass close to 100 TeV. Such theories can have an ultraviolet completion in unified SU(5) theories, we find that this requirement can strongly constrain such composite DM theories as well as give novel predictions for DM cosmology.