Comprehensively Constraining Ultra-Light Primordial Black Holes Through Relic Formation and Early Mergers

Abstract: We investigate constraints on the least explored, smallest mass scales of primordial black holes (PBHs), which evaporate prior to Big Bang Nucleosynthesis (BBN). Our study examines the impact of Planck-mass relics on the allowed fraction of dark matter composed of PBHs ($f_{PBH}$), as well as on the resulting stochastic gravitational wave background and the formation of primordial binaries. We discuss how these binaries and early mergers lead to longer PBH lifetimes, extending the reach of the stringent BBN constraints to smaller masses than usually expected. We make comprehensive constraint plots on the collapse fraction $\beta$ and $f_{PBH}$ (including relics), focusing on ultra-light PBHs.