Axion misalignment driven to the hilltop

Abstract

The QCD axion serves as a well-motivated dark matter candidate and the misalignment mechanism is known to reproduce the observed abundance with a decay constant fa ≃ mathcal{O} (1012) GeV for a misalignment angle θmis ≃ mathcal{O} (1). While fa ≪ 1012 GeV is of great experimental interest, the misalignment mechanism requires the axion to be very close to the hilltop, i.e. θmis ≃ π. This particular choice of θmis has been understood as fine-tuning the initial condition. We offer a dynamical explanation for θmis ≃ π in a class of models. The axion dynamically relaxes to the minimum of the potential by virtue of an enhanced mass in the early universe. This minimum is subsequently converted to a hilltop because the CP phase of the theory shifts by π when one contribution becomes subdominant to another with an opposite sign. We demonstrate explicit and viable examples in supersymmetric models where the higher dimensional Higgs coupling with the inflaton naturally achieves both criteria. Associated phenomenology includes a strikingly sharp prediction of 3 × 109 GeV ≲ fa ≲ 1010 GeV and the absence of isocurvature perturbation.