Robust μ-distortion constraints on primordial supermassive black holes from cubic (gNL) non-Gaussian perturbations

We make the first calculation of the spectral distortion constraints on the primordial curvature power spectrum in the limit of large cubic non-Gaussianity. This calculation involves computing a 2-loop integral, which we perform analytically. Despite being non-perturbatively non-Gaussian, we show that the constraints only change significantly from the case of Gaussian perturbations in the high-k tail, where spectral distortions become weak. We conclude that generating primordial supermassive black holes requires even more extreme forms of non-Gaussianity. We also argue why the mu-distortion constraint is unlikely to significantly change even in the presence of more extreme local non-Gaussianity.