Constraining viscous dark matter in light of CMB spectral distortion

We calculate the $\ensuremath{\mu}$ and $y$-type spectral distortions of cosmic microwave background (CMB), taking a nonstandard interaction between baryons and viscous dark matter. Using the CMB spectral distortion observations, we can constrain any exotic mechanism that may change the energy of the CMB photon, leading to a CMB spectrum distortion. Depending on the viscosity of dark matter, the energy transfer between dark matter and baryons may modify, leading to a modification in CMB distortion. The existing Cosmic Background Explorer/Far Infrared Absolute Spectrophotometer and the Primordial Inflation Explorer (PIXIE) set limits on $y$ and $\ensuremath{\mu}$ types of distortions to $y=1.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$, $\ensuremath{\mu}=9.0\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$ and $y={10}^{\ensuremath{-}8}$, $\ensuremath{\mu}=5.0\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}8}$, respectively. In this paper, we discuss the prerecombination contributions to $\ensuremath{\mu}$ and $y$-type distortions by viscous dark matter and constrain the parameter space using PIXIE bounds on spectral distortion.