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The BICEP2 experiment determined the Hubble parameter during inflation to be about 1014 GeV. Such high inflation scale is in tension with the QCD axion dark matter if the Peccei–Quinn (PQ) symmetry remains broken during and after inflation, because too large axion isocurvature perturbations would be generated. The axion isocurvature perturbations can be suppressed if the axion acquires a sufficiently heavy mass during inflation. We show that this is realized if the PQ symmetry is explicitly broken down to a discrete symmetry and if the breaking is enhanced during inflation. We also show that, even when the PQ symmetry becomes spontaneously broken after inflation, such a temporarily enhanced PQ symmetry breaking relaxes the constraint on the axion decay constant.
Higaki et al. (Wed,) studied this question.