Dark Matter Density Spikes around Primordial Black Holes
  We show that density spikes begin to form from dark matter particles around
primordial black holes immediately after their formation at the
radiation-dominated cosmological stage. This follows from the fact that in the
thermal velocity distribution of particles there are particles with low
velocities that remain in finite orbits around black holes and are not involved
in the cosmological expansion. The accumulation of such particles near black
holes gives rise to density spikes. These spikes are considerably denser than
those that are formed later by the mechanism of secondary accretion. The
density spikes must be bright gamma-ray sources. Comparison of the calculated
signal from particle annihilation with the Fermi-LAT data constrains the
present-day cosmological density parameter for primordial black holes with
masses $M_{\rm BH}\geq10^{-8}M_\odot$ from above by values from $\Omega_{\rm
BH}\leq1$ to $\Omega_{\rm BH}\leq10^{-8}$, depending on $M_{\rm BH}$. These
constraints are several orders of magnitude more stringent than other known
constraints.
