Imprints of the Early Universe on Axion Dark Matter Substructure

Despite considerable experimental progress large parts of the axion-like particle (ALP) parameter space remain difficult to probe in terrestrial experiments. In some cases, however, small-scale structure of the ALP dark matter (DM) distribution is strongly enhanced, offering opportunities for astrophysical tests. Such an enhancement can be produced by a period of pre-nucleosynthesis early matter domination (EMD). This cosmology arises in many ultraviolet completions and generates the correct relic abundance for weak coupling $f_a\sim 10^{16}$ GeV, ALP masses in the range $10^{-13}$ eV $<m_a < 1$ eV, and without fine-tuning of the initial misalignment angle. This range includes the QCD axion around $10^{-9}-10^{-8}$ eV. EMD enhances the growth of ALP small-scale structure, leading to the formation of dense ALP miniclusters. We study the interplay between the initial ALP oscillation, reheating temperature, and effective pressure to provide analytic estimates of the minicluster abundance and properties. ALP miniclusters in the EMD cosmology are denser and more abundant than in $\Lambda$CDM. While enhanced substructure generically reduces the prospects of direct detection experiments, we show that pulsar timing and lensing observations can discover these minihalos over a large range of ALP masses and reheating temperatures.