Dissipation of primordial gravitational waves into CMB spectral distortions: theory and observation prospects

Primordial gravitational waves (PGWs) from inflation can leave observable imprints in the Cosmic Microwave Background (CMB), not only as B-mode polarization but also as spectral distortions (SDs), i.e. tiny deviations from the blackbody spectrum. These distortions, caused by inefficient thermalization in the early plasma, probe primordial perturbations on smaller scales (k ∼ 50–10⁴ 1/Mpc) than those accessible by CMB anisotropies or galaxy surveys. PGWs can even generate distortions at k > 10⁴ 1/Mpc, revealing unexplored early-Universe physics, though their amplitudes are expected to be much lower than scalar-induced ones. To study the SDs induced by the dissipation of PGWs, we modified the CLASS code to compute the energy injected into the primordial plasma by this process.. This implementation allowed for the Green’s function method to be applied to PGWs for the first time, providing an exact treatment of the μ–y transition. We found that large-scale PGWs (k ∼ 10⁻³–10⁻¹ 1/Mpc) re-entering the horizon during this era can enhance μ-distortions by a factor of two for nearly scale-invariant spectra. We also analyzed a log-normal bump in the PGW power spectrum at 10 1/Mpc. For amplitudes ∼ 10⁻³–10⁻² and widths 0.1–1, distortions comparable to scalar-induced ones can arise. Increasing the width broadens the overlap with the μ window function, leading to a saturation of the SD amplitude. Finally, we forecast the science capabilities of a PIXIE-like experiment on the tensor power spectrum by a Markov Chain Monte Carlo (MCMC) analysis. We combined data from BICEP/Keck 2018 and a PIXIE-like experiment to constraint the tensor-to-scalar ratio at two scales. Then, using only PIXIE-like data, we constrained the amplitude of a log-normal bump. This work demonstrates, for the first time, that PGW-induced spectral distortions can jointly constrain the tensor power spectrum with CMB polarization, opening new possibilities for combined analyses with Planck and future missions.