Robust $\mu$-distortion constraints on primordial supermassive black holes from non-Gaussian perturbations

Explaining the origin of supermassive black holes via a primordial origin is severely challenged by the tight spectral distortion constraints on the amplitude of the primordial perturbations. Following the first calculation of how the $\mu$ constraints are modified by non-Gaussianity in a companion paper, we here make the first robust constraints on primordial black hole formation under large non-Gaussianity. Even the infinite $f_{\rm NL}$ limit is insufficiently non-Gaussian but much higher-order non-Gaussianity of the form ${\cal R}={\cal R}_{\rm G}^5$ may allow the formation of any mass primordial black hole without conflicting with distortion constraints. We caution that such extreme models face other challenges.