Constraints on dark matter interactions with standard model particles from CMB spectral distortions

We propose a new method to constrain elastic scattering between dark matter (DM) and standard model particles in the early Universe. Direct or indirect thermal coupling of non-relativistic DM with photons leads to a heat sink for the latter. This results in spectral distortions of the cosmic microwave background (CMB), the amplitude of which can be as large as a few times the DM-to-photon number ratio. We compute CMB spectral distortions due to DM-proton, DM-electron and DM-photon scattering for generic energy-dependent cross sections and DM mass m_DM >~ 1 keV. Using FIRAS measurements we set constraints on the cross sections for m_DM <~ 0.1 MeV. In particular, for energy-independent scattering we obtain sigma[DM-proton] <~ 10^(-24) cm^2 (keV/m_DM)^(1/2), sigma[DM-electron] <~ 10^(-27) cm^2 (keV/m_DM)^(1/2) and sigma[DM-photon] <~ 10^(-39) cm^2 (m_DM/keV). An experiment with the characteristics of PIXIE would extend the regime of sensitivity up to masses m_DM ~ 1 GeV.