Primordial black holes in the early Univese, quantum-gravitational corrections and inflationary cosmology

In essence, primordial black holes generated in the early Universe as a result of a gravitational collapse of the high-density matter are detectors of the processes proceeding in it. As these black holes are generated at high energies (close to the Planck energies) and their radii are small, there is a need to take into consideration the quantum-gravitational corrections for them. In this paper, within the scope of the Generalized Uncertainty Principle, the author continues a study of the quantum-gravitational corrections and their contributions into the inflationary parameters for primordial black holes in the pre-inflationary epoch. Specifically, within this pattern, the author considers a case of Hawking’s radiation (evaporation) for the above-mentioned black holes and derives formulae for the corresponding changes (”shifts”) of the basic inflation parameters. In all cases the expressions for the corresponding correction of е-foldings in an inflation model have been found. In conclusion the main problems for further studies are formulated.