Considerable theoretical efforts have gone into expanding the reach of the quantum chromodynamics (QCD) axion beyond its canonical mass–decay-constant relation. The $Z_{\mathcal{N}}$ QCD axion model reduces the QCD axion mass naturally, by invoking a discrete $Z_{\mathcal{N}}$ symmetry through which the axion field is coupled to $\mathcal{N}$ copies of the Standard Model. Before the QCD phase transition at temperature $T_{\mathrm{QCD}}$, the $Z_{\mathcal{N}}$ potential has a minimum at misalignment angle $\theta =\pi$. At $T_{\mathrm{QCD}}$, $\theta =\pi$ becomes a maximum; the axion potential becomes exponentially suppressed and develops $\mathcal{N}$ minima—only one of which actually solves the strong $CP$ problem. Before $T_{\mathrm{QCD}}$, $\theta$ relaxes toward $\pi$. After $T_{\mathrm{QCD}}$, the axion field starts from around the hilltop and may have sufficient kinetic energy to overcome the newly suppressed potential barriers. Such a field evolution leads to nonperturbative effects via the self-interactions near the hilltop, which can cause the exponential growth of fluctuations and backreaction on the coherent motion. This behavior can influence the relic density of the field and the minimum in which it settles. We conduct the first lattice simulations of the $Z_{\mathcal{N}}$ QCD axion using $\mathcal{C}$osmo$\mathcal{L}$attice to accurately calculate dark matter abundances and find nonperturbative dynamics reduce the abundance by up to a factor of two. We furthermore find that the probability of solving the strong $CP$ problem tends to diverge considerably from the naïve expectation of $1/\mathcal{N}$.

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• Axions
• Cosmology
• Hypothetical particle physics models
• Hypothetical particle production
• Particle dark matter
• Phenomenology