Axions are some of the best motivated particles beyond the Standard Model. We show how the attractive self-interactions of dark matter (DM) axions over a broad range of masses, from $10^{-22}$ eV to $10^7$ GeV, can lead to nongravitational growth of density fluctuations and the formation of bound objects. This structure formation enhancement is driven by parametric resonance when the initial field misalignment is large, and it affects axion density perturbations on length scales of order the Hubble horizon when the axion field starts oscillating, deep inside the radiation-dominated era. This effect can turn an otherwise nearly scale-invariant spectrum of adiabatic perturbations into one that has a spike at the aforementioned scales, producing objects ranging from dense DM halos to scalar-field configurations such as solitons and oscillons. We call this class of cosmological scenarios for axion DM production the large-misalignment mechanism. We explore observational consequences of this mechanism for axions with masses up to $10$ eV. For axions heavier than $10^{-5}$ eV, the compact axion halos are numerous enough to significantly impact Earth-bound direct detection experiments, yielding intermittent but coherent signals with repetition rates exceeding one per decade and crossing times less than a day. These episodic increases in the axion density and kinematic coherence suggest new approaches for axion DM searches, including for the QCD axion. Dense structures made up of axions from $10^{-22}$ eV to $10^{-5}$ eV are detectable through gravitational lensing searches, and their gravitational interactions can also perturb baryonic structures and alter star formation. At very high misalignment amplitudes, the axion field can undergo self-interaction-induced implosions long before matter-radiation equality, producing potentially-detectable low-frequency stochastic gravitational waves.
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