PBH assisted search for QCD axion dark matter

The entropy production prior to BBN era is one of ways to prevent QCD axion with the decay constant $F_{a}\in[10^{12}{\rm GeV},10^{16}{\rm GeV}]$ from overclosing the universe when the misalignment angle is $\theta_{\rm i}=\mathcal{O}(1)$. As such, it is necessarily accompanied by an early matter-dominated era (EMD) provided the entropy production is achieved via the decay of a heavy particle. In this work, we consider the possibility of formation of primordial black holes during the EMD era with the assumption of the enhanced primordial scalar perturbation on small scales ($k>10^{4}{\rm Mpc}^{-1}$). In such a scenario, it is expected that PBHs with axion halo accretion develop to ultracompact minihalos (UCMHs). We study how UCMHs so obtained could be of great use in the experimental search for QCD axion dark matter with $F_{a}\in[10^{12}{\rm GeV},10^{16}{\rm GeV}]$.