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 fo-cus almost exclusively on primordial scalar metric perturbations. Similarly, vector and tensor perturbations should source CMB spectral distortions. In this paper, we give general expres-sions 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 dis-cussion 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 damp-ing 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 2 × 104 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 needs to be included. Key words: Cosmology: CMB – spectral distortions – theory – observations 1