Trading kinetic energy: how late kinetic decoupling of dark matter changes Neff

2019 
Elastic scattering between dark matter particles and a relativistic species such as photons or neutrinos leads to a transfer of energy from the latter due to their intrinsically different temperature scaling relations. In this work, we point out that this siphoning of energy from the radiation bath manifests as a change in the effective number of neutrinos Neff, and compute the expected shift Δ Neff for dark matter-photon and dark matter-neutrino elastic scattering as a function of the dark matter mass mψ and scattering cross section σψ−X. For (mψ,σψ−X)-parameter regions already explored by nonlinear probes such as the Lyman-α forest through collisional and/or free-streaming damping, we find shifts of |Δ Neff| O(10−2), which may be within the reach of the proposed CMB-S4 experiment. For most of the as-yet-unexplored parameter space, however, we expect |Δ Neff| O(10−3). An ideal 21 cm tomography survey of the dark ages limited only by cosmic variance is potentially sensitive to |Δ Neff| O(10−6), in which case dark matter masses up to mψ ~ 10 MeV may be probed via their effect on Neff.
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