A Stepping Stone Solution to the QCD Axion Isocurvature Problem

We propose a ''stepping stone'' realization of the varying Peccei Quinn (PQ) scale solution to the QCD axion isocurvature problem. In conventional implementations, suppressing isocurvature during high scale inflation requires a large inflationary PQ scale, while the subsequent evolution toward the much smaller late time vacuum can induce parametric resonance and nonthermal restoration of the PQ symmetry. We ameliorate this tension by introducing an intermediate PQ-breaking vacuum that is reached before the end of inflation, so that the later evolution to the present day PQ scale spans only a moderate hierarchy. The vacuum structure arises radiatively: a Yukawa coupling between the PQ scalar and PQ-charged fermions drives the quartic coupling negative at high scales while keeping it positive at lower scales. A positive dimension six operator then stabilizes a large field minimum, while the positive low energy quartic together with the quadratic terms generates the intermediate vacuum. We study two mechanisms in which the rolling inflaton removes the large field minimum, either by scanning a hidden non-Abelian gauge coupling or by directly scanning the Yukawa coupling. In both cases the PQ field is released toward the intermediate vacuum during inflation, after CMB modes have exited the horizon. We exhibit benchmark regions with subdominant backreaction on the inflationary sector and suppressed vacuum tunneling, and show that the construction permits substantially less hierarchical quartic and higher-dimensional couplings than conventional realizations that depend on a varying PQ scale. The underlying logic may have analogues for extra-dimensional or string axions, where the effective axion decay constant is controlled by geometric moduli, although realizing the required intermediate vacuum in a controlled modulus potential is nontrivial.