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The most promising mechanism of generating primordial black holes (PBHs) is by the enhancement of power spectrum of the primordial curvature perturbation, which is usually accompanied by the the enhancement of non-Gaussianity that crucially changes the abundance of PBHs. In this review I will discuss how non-Gaussianity is generated in single field inflation as well as in the curvaton scenario, and then discuss how to calculate PBH mass function with such non-Gaussianities. I also show non-Gaussianity only has mild effects on the induced gravitational waves (GWs), which gives robust predictions in the mHz and nHz GW experiments.
Shi Pi (Tue,) studied this question.
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