Dynamical Axion Misalignment from the Witten Effect

Abstract

We propose a relaxation mechanism for the initial misalignment angle of the pre-inflationary QCD axion with a large decay constant. The proposal addresses the challenges posed to the axion dark matter scenario by an overabundance of axions overclosing the Universe, as well as by isocurvature constraints. Many state-of-the-art experiments are searching for QCD axion dark matter with a decay constant as large as $10^{16}\,\mathrm{GeV}$, motivating the need for a theoretical framework such as ours. In our model, hidden sector magnetic monopoles generated in the early Universe give the axion a large mass via the Witten effect, causing early oscillations that reduce the misalignment angle and axion abundance. As the hidden gauge symmetry breaks, its monopoles confine via cosmic strings, dissipating energy into the Standard Model and leading to monopole-antimonopole annihilation. This removes the monopole-induced mass, leaving only the standard QCD term. We consider the symmetry breaking pattern of $\mathrm{SU}(2)' \to \mathrm{U}(1)' \to 1$, leading to monopole and string formation respectively. We calculate the monopole abundance, their interactions with the axion field, and the necessary conditions for monopole-induced axion oscillations, while accounting for UV instanton effects. We present three model variations based on different symmetry breaking scales and show that they can accommodate an axion decay constant of up to $10^{16}\,\mathrm{GeV}$ with an inflationary scale of $10^{15}\,\mathrm{GeV}$. The required alignment between monopole-induced and QCD axion potentials is achieved through a modest Nelson-Barr mechanism, avoiding overclosure without anthropic reasoning.