ALP Dark Matter in a Primordial Black Hole Dominated Universe

We investigate the phenomenological consequences of axion-like particle (ALP) dark matter with an early matter domination triggered by primordial black holes (PBHs). We focus on light BHs with masses smaller than $\sim 10^9~$g which fully evaporate before Big Bang nucleosynthesis. We numerically solve the coupled Boltzmann equations, carefully taking the greybody factors and BH angular momentum into account. We find that the entropy injection from PBH evaporation dilutes the ALP relic abundance originally produced via the vacuum misalignment mechanism, opening the parameter space with larger scales $f_a$ or, equivalently, smaller ALP-photon couplings $g_{a\gamma}$, within the reach of future detectors as ABRACADABRA, KLASH, ADMX, and DM-Radio. Moreover, the ALP minicluster masses can be several orders of magnitude larger if the early Universe features an PBH dominated epoch. For the relativistic ALPs produced directly from Hawking radiation, we find that their contribution to the dark radiation is within the sensitivity of next generation CMB experiments. For the sake of completeness, we also revisit the particular case of the QCD axion.