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