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_{χ}≳1 keV. Using Far-Infrared Absolute Spectrophotometer measurements, we set constraints on the cross sections for m_{χ}≲0.1 MeV. In particular, for energy-independent scattering we obtain σ_{DM-proton}≲10^{-24} cm^{2} (keV/m_{χ})^{1/2}, σ_{DM-electron}≲10^{-27} cm^{2} (keV/m_{χ})^{1/2}, and σ_{DM-photon}≲10^{-39} cm^{2} (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.