CMB spectroscopy at third-order in cosmological perturbations

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 $\kappa =f_{\mathrm{NL}}^{\mathrm{loc}}\times \mathcal{O}({10}^{-18})$ 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.