Limits on MeV dark matter from the effective number of neutrinos

Abstract

Thermal dark matter that couples more strongly to electrons and photons than to neutrinos will heat the electron-photon plasma relative to the neutrino background if it becomes nonrelativistic after the neutrinos decouple from the thermal background. This results in a reduction in ${N}_{\mathrm{eff}}$ below the standard model value, a result strongly disfavored by current CMB observations. Taking conservative lower bounds on ${N}_{\mathrm{eff}}$ and on the decoupling temperature of the neutrinos, we derive a bound on the dark matter particle mass of ${m}_{\ensuremath{\chi}}>3--9\text{ }\text{ }\mathrm{MeV}$, depending on the spin and statistics of the particle. For $p$-wave annihilation, our limit on the dark matter particle mass is stronger than the limit derived from distortions to the CMB fluctuation spectrum produced by annihilations near the epoch of recombination.