Fine-tuning in mixed Dark Matter models with Primordial Black Hole relics
We investigate the fine-tuning of a tripartite dark matter (DM) scenario involving ultra-light primordial black holes (PBHs), whose evaporation before Big Bang Nucleosynthesis leaves Planck-mass relics and produces DM particles together with an independently produced DM component. We uniformly evaluate the parameter sensitivity required to reproduce the observed DM abundance, $Ω_{\rm DM}$. Considering thermal WIMP freeze-out, freeze-in, and QCD axion misalignment, and assuming PBHs form via collapse of perturbations following horizon entry, we find that the fine-tuning is normally dominated by the structure of the PBH relic abundance calculation rather than by the particle DM candidate or the details of PBH evaporation. In radiation-dominated cosmologies, the DM abundance is highly sensitive to the primordial curvature power spectrum because the PBH formation fraction depends exponentially on density fluctuations. Although an early PBH-dominated era dilutes pre-existing abundances and reduces the apparent tuning of the PBH abundance, inflationary fine-tuning remains required to produce the required initial large amplitude perturbations. We further examine alternative PBH formation channels, including supercooled first-order phase transitions and collapsing domain walls, and find that they replace the inflationary fine-tuning with alternative exponential sensitivities. We conclude that a natural realization of an order unity PBH relic abundance is hard to motivate.