Primordial black hole formation during slow-reheating: A review

In this paper we review the possible mechanisms for the production of primordial black holes (PBHs) during a slow-reheating period {in which the energy transfer of the inflaton field to standard model particles becomes effective at slow temperatures}, offering a comprehensive examination of the theoretical foundations and conditions required for each of formation channel. In particular, we focus on post-inflationary scenarios where there are no self-resonances and the reheating epoch can be described {by the inflaton evolving in} a quadratic-like potential. In the hydrodynamical interpretation of this field during the slow-reheating epoch, the gravitational collapse of primordial fluctuations is subject to conditions on their sphericity, limits on their spin, as well as a maximum velocity dispersion. We show how to account for all conditions and show that PBHs form with different masses depending on the collapse mechanism. Finally we show, through an example, how PBH production serves to probe both the physics after primordial inflation, as well as the primordial powerspectrum at the smallest scales.