Mechanism of Generating Isothermal Perturbation by a StrongCPNonconservation

A large-scale inhomogeneity of coherent axion field may exist in the early universe. This gives a spatially varying source of strong $\mathrm{CP}$ nonconservation and, when coupled to baryon-nonconserving interaction, may lead to generation of the isothermal perturbation of baryon density. A specific mechanism is presented, in which three-body decay of a heavy Majorana lepton gives the additional baryon generation.