In-depth analysis of the clustering of dark matter particles around
  primordial black holes I: density profiles
  Primordial black holes may have been produced in the early stages of the
thermal history of the Universe after cosmic inflation. If so, dark matter in
the form of elementary particles can be subsequently accreted around these
objects, in particular when it gets non-relativistic and further streams freely
in the primordial plasma. A dark matter mini-spike builds up gradually around
each black hole, with density orders of magnitude larger than the cosmological
one. We improve upon previous work by carefully inspecting the computation of
the mini-spike radial profile as a function of black hole mass, dark matter
particle mass and temperature of kinetic decoupling. We identify a phase-space
contribution that has been overlooked and that leads to changes in the final
results. We also derive complementary analytical formulae using convenient
asymptotic regimes, which allows us to bring out peculiar power-law behaviors
for which we provide tentative physical explanations.
