Abstract 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 [Padilla et al., Phys. Rev. D, 106, 023519 (2022)], that draws on the analogy between an extended reheating era and the scalar field dark matter model, contemplating the gravitational collapse of inflaton halos and inflaton stars.