CP violation in QCD, axions and possible connections to dark matter

Sammanfattning: The strong CP problem and its solution are treated on the undergraduate level. We first review the theoretical background of symmetry and symmetry breaking in particle physics. The Goldstone model is treated for several simple systems: the linear sigma model, the Higgs mechanism and the interpretation of pions as pseudo-Goldstone bosons in QCD. The problem of lack of CP-violation in strong interactions is explained, and the most popular solution---the addition of an additional $U(1)_{\mathrm{PQ}}$-symmetric field and its quanta, the axion---is presented. The current experimental status of the axion is detailed, including limits set by laboratory and astrophysical searches. Finally, the axion in the context of its possible role as a dark matter (DM) candidate is reviewed, focusing primarily on the theory of axionic cold dark matter and its status. We find that the axion is an appealing solution to the CP problem, and a highly viable candidate for cold dark matter in the Universe.