Spectral distortions from the dissipation of tensor perturbations
  Spectral distortions of the cosmic microwave background (CMB) may become a powerful probe of primordial perturbations at small scales. Existing studies of spectral distortions focus almost exclusively on primordial scalar metric perturbations. Similarly, vector and tensor perturbations should source CMB spectral distortions. In this paper, we give general expressions for the effective heating rate caused by these types of perturbations, including previously neglected contributions from polarization states and higher multipoles. We then focus our discussion on the dissipation of tensors, showing that for nearly scale invariant tensor power spectra, the overall distortion is some six orders of magnitudes smaller than from the damping of adiabatic scalar modes. We find simple analytic expressions describing the effective heating rate from tensors using a quasi-tight coupling approximation. In contrast to adiabatic modes, tensors cause heating without additional photon diffusion and thus over a wider range of scales, as recently pointed out by Ota et. al 2014. Our results are in broad agreement with their conclusions, but we find that small-scale modes beyond k< 2x10^4 Mpc^{-1} cannot be neglected, leading to a larger distortion, especially for very blue tensor power spectra. At small scales, also the effect of neutrino damping on the tensor amplitude needs to be included. 
Jens Chluba, Liang Dai, Daniel Grin, Mustafa A. Amin, Marc   Kamionkowski
astro-ph.CO hep-th