Robust μ-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 μ 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_ NL limit is insufficiently non-Gaussian but much higher-order non-Gaussianity of the form R= R_ 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.