Cosmic microwave background bounds on primordial black holes including
  dark matter halo accretion
  Even if massive ($10\,M_\odot \lesssim M \lesssim 10^4 M_\odot$) primordial
black holes (PBHs) can only account for a small fraction of the dark matter
(DM) in the universe, they may still be responsible for a sizable fraction of
the coalescence events measured by LIGO/Virgo, and/or act as progenitors of the
supermassive black holes (SMBHs) observed already at high redshift ($z\gtrsim
6$). In presence of a dominant, non-PBH DM component, the bounds set by CMB via
an altered ionization history are modified. We revisit the cosmological
accretion of a DM halo around PBHs via toy models and dedicated numerical
simulations, deriving updated CMB bounds which also take into account the last
Planck data release. We prove that these constraints dominate over other
constraints available in the literature at masses $M\gtrsim 20-50\,M_\odot$
(depending on uncertainty in accretion physics), reaching the level $f_{\rm
PBH}<3\times 10^{-9}$ around $M\sim 10^{4}\,M_\odot$. These tight bounds are
nonetheless consistent with the hypothesis of a primordial origin of the SMBH
massive seeds.
