Cosmic microwave background spectral distortions from Rayleigh
  scattering at second order
  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.
