Axion production via trapped misalignment from Peccei-Quinn symmetry breaking

The Peccei-Quinn (PQ) symmetry does not need to be exact, and even a tiny source of PQ breaking not aligned with the QCD anomaly might have significant phenomenological implications. In this study, we examine the effects of a general class of PQ-breaking operators on the axion cosmological production via misalignment, focussing on both temperature-dependent and independent PQ-breaking potentials. In particular, we show that a variant of the trapped misalignment mechanism can delay the onset of axion oscillation, leading to an axion dark matter window with $m_a \gg 10^{-5}$ eV. This scenario is testable through various experimental approaches, including standard axion haloscopes and helioscopes, as well as searches for electric dipole moments and axion-mediated forces.