Cosmological effects of Peccei-Quinn symmetry breaking on QCD axion dark matter

We study cosmological effects of explicit Peccei-Quinn breaking on the QCD axion dark matter. find that abundance decreases or increases significantly depending initial position, even for a tiny satisfies experimental bound neutron electric dipole measurements. If first starts to oscillate around wrong vacuum and if it gets trapped there until false disappears due non-perturbative effects, its is independent decay constant $f_a$, as pointed out in [JHEP 06 (2016) 150]. Thus, produced by trapping mechanism can explain matter when close lower limit stellar cooling arguments. On other hand, about potential minimum low-energy vacuum, reduced because adiabatic suppression mechanism. This relaxes upper window large values $f_a$. also discuss how axionic isocurvature perturbation affected term, show be suppressed both regimes. In particular, inflation scale relaxed many orders magnitudes $f_a \lesssim 10^{11}{\rm GeV}$ compared conventional scenario.