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.
