Detuning primordial black hole dark matter with early matter domination and axion monodromy

We present a scenario that ameliorates the tuning problems present in models of primordial black hole dark matter from inflation. Our setup employs the advantages of gravitational collapse in a long epoch of early matter domination with reheating temperature $\lesssim 10^{6}~\text{GeV}$. Furthermore, we make use of a string-inspired class of models where the inflaton is identified with a non-compact axion field. In this framework, the presence of multiple local minima in the inflaton potential can be traced back to an approximate discrete shift symmetry. This scenario allows the formation of primordial black holes in the observationally viable range of masses ($M_{\text{PBH}}\sim 10^{-13}M_{\odot}-10^{-16}M_{\odot}$) accounting for all dark matter, and in excellent agreement with the CMB. Crucially, we find a significant reduction in the required tuning of the parameters of the inflationary potential, in contrast to the standard case of primordial black hole formation during radiation domination. However, abundant formation of light PBHs during an early phase of matter domination can be more easily in conflict with evaporation bounds. We discuss how these can be avoided under mild assumptions on the collapsing energy density fraction.