Robust {\mu}-distortion constraints on primordial supermassive black holes from cubic (gNL) non-Gaussian perturbations

TL;DR

This paper calculates spectral distortion constraints on the primordial curvature power spectrum considering large cubic non-Gaussianity, revealing that constraints are similar to Gaussian cases except at high wavenumbers, impacting supermassive black hole formation.

Contribution

First analytical calculation of spectral distortion constraints with large cubic (gNL) non-Gaussianity, extending understanding of primordial black hole formation conditions.

Findings

Constraints only significantly differ in high-k tail regions.

Generating supermassive black holes requires extreme non-Gaussianity.

Mu-distortion constraints remain robust against local non-Gaussianity variations.

Abstract

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.