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
$\kappa=f^{\rm loc.}_{\rm NL}\times \mathcal O(10^{-18})$ 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.
