DM Interactions: Complementarity of different probes
Key point of relevance to CMB-S4: the CMB constraint will improve a lot with small-scale polarization measurements, and will enter parameter space inaccessible by nuclear-recoil direct-detection measurements.
In more detail, the CMB anisotropies are sensitive to the energy injection from DM-baryon scattering, and can probe the same DM-baryon interactions as direct detection. There is strong complementarity between these approaches: i) they probe the same physics in two different settings---direct detection locally, and CMB in the early universe; ii) direct detection relies on assumptions about local astrophysical properties of DM particles and on complicated modeling of nuclear-response functions, while the CMB is not subject to the same limitations; iii) nuclear-recoil measurements in direct detection have a kinematic limitation to probing DM mass above a few GeV, while CMB-S4 measurements gain sensitivity at lower masses.
Complementarity between direct detection and CMB measurements is illustrated in the plot below on the example of "millicharge dark matter". This plot shows current constraints, from direct detection (blue shaded; taken from Gluscevic et al (2015)), and from Planck temperature+Lyman alpha forest observations (green shaded; constraint is implied from the limit on model case from Dvorkin et al (2014)). Note that the previous analysis stops at roughly 1 GeV, and does not include CMB polarization. Vera and Kim Boddy are working on including analysis of polarization and going to lower mass (which will push the CMB constraint down and to the left) and on producing a constraint for all possible DM interactions within the effective theory of DM. Cora is also working on extending previous work to lower masses.