Abstract
Primordial black holes (PBHs) form from large-amplitude initial density
fluctuations and may comprise some or all of the dark matter. If PBHs have an
extended mass spectrum, or in mixed PBH-particle dark matter scenarios, the
extreme density fluctuations necessary to produce PBHs also lead to the
formation of a much greater abundance of dark matter minihaloes with internal
densities potentially of order $10^12$ M$_ødot$ pc$^-3$. We develop an
analytic description of the formation of these ultradense haloes and use it to
quantitatively compare PBH and halo distributions. PBHs that contribute only a
per cent level fraction of the dark matter are accompanied by ultradense haloes
that nevertheless comprise an order-unity fraction. This finding significantly
alters the predictions of many PBH scenarios, enabling a variety of new
observational tests.
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