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 \textrm { 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 .