Xavier Pritchard, Christian T. Byrnes, Julien Lesgourgues, Devanshu Sharma

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.