Nonthermal histories for the early universe have received notable attention as they are a rich source of phenomenology, while also being well motivated by top-down approaches to beyond the Standard Model physics. The early (pre-big bang nucleosynthesis) matter phase in these models leads to enhanced growth of density perturbations on sub-Hubble scales. Here, we consider whether primordial black hole formation associated with the enhanced growth is in conflict with existing observations. Such constraints depend on the tilt of the primordial power spectrum, and we find that nonthermal histories are tightly constrained in the case of a significantly blue spectrum. Alternatively, if dark matter is taken to be of nonthermal origin, we can restrict the primordial power spectrum on scales inaccessible to cosmic microwave background and large scale structure observations. We establish constraints for a wide range of scalar masses (reheat temperatures) with the most stringent bounds resulting from the formation of ${10}^{15}\mathrm{g}$ black holes. These black holes would be evaporating today and are constrained by FERMI observations. We also consider whether the breakdown of the coherence of the scalar oscillations on subhorizon scales can lead to a Jean’s pressure preventing black hole formation and relaxing our constraints. Our main conclusion is that primordial black hole constraints, combined with existing constraints on nonthermal weakly interacting massive particles, favor a primordial spectrum closer to scale invariance or a red tilted spectrum.

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• Big bang nucleosynthesis
• Dark matter
• Astronomical black holes
• Weakly interacting massive particles