Axions in the Presence of Gauge Theories Beyond the Standard Model

Non-supersymmetric Grand Unified $SO(10)\times U(1)_{\rm PQ}$ models have all the ingredients to solve several fundamental problems of particle physics and cosmology -- neutrino masses and mixing, baryogenesis, the non-observation of strong CP violation, dark matter, inflation -- in one stroke. The axion -- the pseudo Nambu-Goldstone boson arising from the spontaneous breaking of the $U(1)_{\rm PQ}$ Peccei-Quinn symmetry -- is the prime dark matter candidate in this setup. We work out the constraints imposed on the axion mass by gauge coupling unification. We also discuss the cosmological and phenomenological implications.\\We consider the described models in the larger context set by combining the Peccei-Quinn symmetry with new gauge symmetries in different ways. We classify the relevant models and give a general procedure by which the physical axion must be identified. Additionally, we apply this procedure to multiple examples. Finally, we discuss the possibility of obtaining the Peccei-Quinn symmetry as an accidental symmetry