Mounting evidence suggests that the semiclassical description of a black hole breaks down at the latest after losing an $O(1)$ fraction of its mass. As a result, effects such as memory burden can slow down evaporation so that small primordial black holes (PBHs), in particular those in the mass range ${10}^6\mathrm{g}$ to ${10}^9\mathrm{g}$, become viable dark matter candidates. In this paper, we investigate the production of PBHs from a prototype model of polynomial inflation with a nonminimal coupling to gravity. We show that a sufficiently small PBH mass alleviates any tension with cosmic microwave background observations. Moreover, we develop efficient numerical procedures to identify model parameters and evolve Mukhanov-Sasaki modes to place bounds on the scalar-induced stochastic gravitational wave (GW) background. While we identify some prospects for observation with future GW detectors, our results highlight the need to develop new experiments for high-frequency GW detection in the $\sim \mathrm{kHz}$ to $\sim \mathrm{MHz}$ range. Finally, we demonstrate that previously used Ansätze for modeling the power spectrum only yield a reliable approximation for the GW signal if some input from inflation is used.

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• Dark matter
• Gravitational wave sources
• Inflation
• Primordial black holes