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 stems 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 (BH) a parts per thousand yen 10(-8) M (aS (TM)) from above by values from Omega(BH) a parts per thousand currency sign 1 to Omega(BH) a parts per thousand currency sign 10-8, depending on MBH. These constraints are several orders of magnitude more stringent than other known constraints.