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Primordial Black Holes as Dark Matter: Almost All or Almost Nothing

Primordial black holes (PBHs) are expected to accrete particle dark matter around them to form ultracompact minihalos (UCMHs), if the PBHs themselves are not most of the dark matter. We show that if most dark matter is a thermal relic, then the inner regions of UCMHs around PBHs are highly luminous sources of annihilation products. Flux constraints on gamma rays and neutrinos set strong abundance limits, improving previous limits by orders of magnitude. Assuming enough particle dark matter exists to form UCMHs, we find that Omega_PBH <~ 10^-4 (for m_DM c^2 ~ 100 GeV) for a vast range in PBH mass. We briefly discuss the uncertainties on our limits, including those due to the evolution of the UCMH luminosity as it annihilates.