Cosmic microwave background spectral distortions from Rayleigh scattering at second order

Abstract

Cosmic microwave background (CMB) spectral distortion from Rayleigh scattering is calculated for the first time in rigorous second-order cosmological perturbation theory. The new spectral distortion is sensitive to acoustic dissipation at $10^{-2}<k{\rm Mpc}/h<1$, which slightly extends the scale constrained by the CMB anisotropies. The spectral shape is different from either temperature perturbations or any other traditional spectral distortions from Compton scattering, such as $y$ and $\mu$. The new spectral distortion is not formed in the late Universe, unlike the thermal Sunyaev-Zel'dovich effect degenerated with the primordial $y$ distortions since photons must be hot for Rayleigh scattering. Therefore, ideal measurements can distinguish the signal from the other effects and extract new information during recombination. Assuming cosmological parameters consistent with the recent CMB anisotropy measurements, we find the new spectral distortion is $6.5\times 10^{-3}$Jy/str, which is one order of magnitude smaller than the currently proposed target sensitivity range of voyage 2050.