Production of PBHs from inflaton structure

At times prior to Big Bang Nucleosynthesis, the universe could show a primordial structure formation period if dominated by a fast oscillating inflaton field during reheating. In this context, we have postulated a new mechanism of primordial black hole formation [L. E. Padilla, J. C. Hidalgo, and K. A. Malik, Phys. Rev. D, vol. 106, p. 023519, Jul 2022], that draws the analogy between an extended reheating era and the scalar field dark matter model, stipulating the gravitational collapse of inflaton halos and inflaton stars. In this paper we look at the requirements for the realization of this new mechanism. We show that a generic primordial power spectrum with a peak at small scales is most suitable for the production of a considerable number of PBHs. When such requirement is met, and if reheating lasts long enough, large populations of PBHs with $M_{\rm PBH}\sim 1~\mathrm{gram}$ may be produced. We find in particular, that the mass fraction of PBHs is orders of magnitude larger than that obtained when PBHs form via direct collapse in a universe dominated by radiation or pressure-less dust. Looking at observable implications of our findings, we explore the possibility that the PBHs component may dominate the energy density of the universe at some point after the end of reheating.