Microlensing constraints on clustered primordial black holes

Abstract: The discovery of black-hole-binary mergers through their gravitational wave (GW) emission has reopened the exciting possibility that dark matter is made, at least partly, of primordial black holes (PBHs). However, this scenario is challenged by many observational probes that set bounds on the relative PBH abundance across a broad range of viable PBH masses. Among these bounds, the ones coming from microlensing surveys lead to the strongest constraints in the mass range from $\sim 10^{-10}$ to a few M$_{\odot}$. The upper part of this range precisely corresponds to the mass window inside which the formation of PBHs should be boosted due to the QCD phase transition in the early Universe, which makes the microlensing probes particularly important. However, it has been argued that taking into account the inevitable clustering of PBH on small scales can significantly relax or entirely remove these bounds. While the impact of PBH clustering on the GW event rate has been studied in detail, its impact on the microlensing event rate has not yet been fully assessed. In this Letter, we address this issue, and show that clusters arising from isocurvature perturbations, that originating from PBHs formed from Gaussian initial curvature perturbations, do not alter the current microlensing constraints, as they are not sufficiently compact.