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Axion-like particles (ALPs) are leading candidates to explain the dark matterin the universe. Their production via the misalignment mechanism has beenextensively studied for cosine potentials characteristic ofpseudo-Nambu-Goldstone bosons. In this work we investigate ALPs withnon-periodic potentials, which allow for large misalignment of the field fromthe minimum. As a result, the ALP can match the relic density of dark matter ina large part of the parameter space. Such potentials give rise toself-interactions which can trigger an exponential growth of fluctuations inthe ALP field via parametric resonance, leading to the fragmentation of thefield. We study these effects with both Floquet analysis and latticesimulations. Using the Press-Schechter formalism, we predict the halo massfunction and halo spectrum arising from ALP dark matter. These halos can bedense enough to produce observable gravitational effects such as astrometriclensing, diffraction of gravitational wave signals from black hole mergers,photometric microlensing of highly magnified stars, perturbations of stars inthe galactic disk or stellar streams. These effects would provide a probe ofdark matter even if it does not couple to the Standard Model. They would not beobservable for halos predicted for standard cold dark matter and for ALP darkmatter in the standard misalignment mechanism. We determine the relevantregions of parameter space in the (ALP mass, decay constant)-plane and comparepredictions in different axion fragmentation models.

ALP dark matter with non-periodic potentials: parametric resonance, halo formation and gravitational signatures