The Apparent Universe, Inflation Cosmology and Primordial Black Holes within the Scope of GUP

Entropic corrections within the scope of the Generalized Uncertainty Principle are applied to the apparent Universe with zero curvature in a study of inflation models. It is demonstrated that the corresponding quantum-gravity deformation of the inflation potential is also the inflation potential that, within low energies far from the Planck energies, is coincident with the initial one. With the inflation pattern, in slow roll regime this leads to an increase of the number of e-foldings as compared to the semi-classical consideration. It is shown that in this case for hybrid inflation the probability of the origination of primordial black holes (pbhs) decreases at the last stage of inflation. In conclusion it is noted that the derived formulae may be used to compute the quantum-gravity corrections for pbhs originating in the De Sitter space during the pre-inflation era as well the corresponding quantities, specifically for the scale-invariant power spectrum of a scalar field from small pbhs. Briefly, further steps associated with application of the methods considered are discussed.