Axion dark matter with high-scale inflation

We show that supersymmetric axion models breaking the PQ symmetry by the interplay of non-renormalizable supersymmetric terms and soft supersymmetry breaking terms provide a natural framework not only for generating the axion scale from soft supersymmetry breaking scale m3/2m3/2 but also for enhancing it during inflation by factor of order HI/m3/2 where HI≃1014 GeVHI≃1014 GeV according to the recent BICEP2 result. In this scheme, the PQ symmetry can stay broken throughout the whole history of the Universe if the reheat temperature is below 1010 GeV1010 GeV, or m3/2m3/2 when the PQ fields couple strongly to thermal (Standard Model) particles. It is also shown that parametric resonance during preheating is not effective enough to induce non-thermal PQ symmetry restoration. As a consequence, axion models with the QCD anomaly NDW>1NDW>1 can be made free from the domain wall problem while the axion isocurvature perturbation is suppressed sufficiently for the axion scale during inflation larger than about MP(Ωah2/0.12)1/2(Fa/1012 GeV)0.6 GeVMP(Ωah2/0.12)1/2(Fa/1012 GeV)0.6 GeV.