Role of the equivalence principle in gauge and axial symmetries of Yukawa coupling, and the strong CP problem

It is demonstrated the fundamental role of the equivalence principle in gravity for the Yukawa coupling between scalar and fermion fields. The Kibble-Zurek mechanism for formation of topological defects as vortexes and monopoles breaks down in system with a global gauge symmetry only. At the same time, the different vacuums can occur, which are separated be domain walls. The equivalence principle makes the strong violation of CP invariance impossible. Thus the axion hypothesis becomes redundant.