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 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(NL)(loc) x 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.