Primordial Black Holes (PBHs) and The Signatures of Cosmic Non-Gaussianity

Abstract: Primordial black holes (PBHs) provide a unique probe of the small-scale primordial Universe and may constitute a fraction of the dark matter. Their formation is highly sensitive to non-Gaussian features in the primordial curvature perturbation $\zeta$. In this work we investigate PBH production in the curvaton scenario, where the decay of a late-time light scalar field imprints large, inherently non-Gaussian fluctuations on small scales. Using the exact non-linear mapping between the Gaussian curvaton field perturbations and $\zeta$, we compute the full non-perturbative probability distribution functions of $\zeta$ and derive the PBH formation fraction $\beta$ without relying on a truncated non-Gaussian expansion. We show that the enhanced tail of the distribution dramatically amplifies PBH production, leading to an exponential sensitivity of $\beta$ to the curvaton decay fraction $\Omega_{\chi,\rm dec}$. By modeling the scale dependence of curvaton fluctuations with a lognormal profile, we obtain realistic, extended PBH mass spectra rather than monochromatic peaks. We further highlight the associated stochastic gravitational-wave background induced at second order, whose peak frequency correlates directly with the PBH mass scale. Our results demonstrate that the curvaton scenario naturally produces a rich phenomenology of PBHs and gravitational waves, sharply distinct from Gaussian single-field inflation models, and provide a framework for connecting small-scale non-Gaussian physics to upcoming gravitational-wave and PBH observations.