We propose a QCD axion model where the origin of PQ symmetry and suppression of axion isocurvature perturbations are explained by introducing an extra dimension. Each extra quark-antiquark pair lives on branes separately to suppress PQ breaking operators. The size of the extra dimension changes after inflation due to an interaction between inflaton and a bulk scalar field, which implies that the PQ symmetry can be drastically broken during inflation to suppress undesirable axion isocurvature fluctuations.
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Kawasaki et al. (2015) studied this question.
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