Constraints on Dark Matter Interactions with Standard Model Particles from Cosmic Microwave Background 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 nonrelativistic 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_χ1 keV. Using Far-Infrared Absolute Spectrophotometer measurements, we set constraints on the cross sections for m_χ0.1 MeV. In particular, for energy-independent scattering we obtain σDM-proton10^-24 cm² (keV/m_χ)1/2, σDM-electron10^-27 cm² (keV/m_χ)1/2, and σDM-photon10^-39 cm² (m_χ/keV). An experiment with the characteristics of the Primordial Inflation Explorer would extend the regime of sensitivity up to masses m_χ~1 GeV.