CMB spectroscopy at third-order in cosmological perturbations

TL;DR

This paper introduces a third-order spectral distortion, $$, in the CMB caused by mode coupling from primordial non-Gaussianity, revealing a tiny but unique frequency-dependent signal sensitive to squeezed bispectra shapes.

Contribution

The authors compute the third-order spectral distortion  in the CMB, linking it to primordial non-Gaussianity and mode coupling, a novel theoretical development.

Findings

 is proportional to local non-Gaussianity parameter $f^{ m loc.}_{ m NL}$ with an estimated magnitude of   10^{-18}.

 exhibits a distinct frequency dependence from other spectral distortions.

 is sensitive to squeezed bispectra shapes not constrained by CMB anisotropies.

Abstract

Early energy injection to the Cosmic Microwave Background (CMB) from dissipation of acoustic waves generates deviations from the blackbody spectrum not only at second-order but also at third-order in cosmological perturbations. We compute this new spectral distortion $\mathcal \kappa$ based on third-order cosmological perturbation theory and show that $\kappa$ arises as a result of mode coupling between spectral distortions and temperature perturbations. The ensemble average of $\kappa$ can be directly sourced by (integrated) primordial non-Gaussianity. In particular, we roughly estimate the signal as $\kappa=f^{\rm loc.}_{\rm NL}\times \mathcal O(10^{-18})$ for local type scale-independent non-Gaussianity. The signal is incredibly tiny; however, we argue that it carries a specific frequency dependence different from other types of CMB spectral distortions. Also, it should be noticed that $\kappa$ is sensitive to extremely squeezed shapes of primordial bispectra that cannot be constrained by the CMB anisotropies. Finally, we comment on other possible applications of our results.