If the symmetry breaking responsible for axion dark matter production occurs during the radiation-dominated epoch in the early Universe, then this produces large amplitude perturbations that collapse into dense objects known as axion miniclusters. The characteristic minicluster mass, $M_0$, is set by the mass inside the horizon when axion oscillations begin. For the QCD axion $M_0\sim {10}^{-10}{M}_{\odot }$, however, for an axionlike particle, $M_0$ can approach $M_{\odot }$ or higher. Using the Press-Schechter formalism we compute the mass function of halos formed by hierarchical structure formation from these seeds. We compute the concentrations and collapse times of these halos and show that they can grow to be as massive as $10^6{M}_0$. Within the halos, miniclusters likely remain tightly bound, and we compute their gravitational microlensing signal taking the fraction of axion dark matter collapsed into miniclusters, $f_{\mathrm{MC}}$, as a free parameter. A large value of $f_{\mathrm{MC}}$ severely weakens constraints on axion scenarios from direct detection experiments. We take into account the non-Gaussian distribution of sizes of miniclusters and determine how this affects the number of microlensing events. We develop the tools to consider microlensing by an extended mass function of nonpointlike objects, and we use microlensing data to place the first observational constraints on $f_{\mathrm{MC}}$. This opens a new window for the potential discovery of the axion.

• Received 4 August 2017

DOI:https://doi.org/10.1103/PhysRevD.97.083502