A lower bound on the mass of cold thermal dark matter from Planck

We show that the new measurement of the effective number of neutrinos (N-eff) by the Planck satellite can be used to set a robust lower bound on the mass of cold thermal dark matter of O(MeV). Our limit applies if the dark matter remains in thermal equilibrium by coupling to electrons and photons or through interactions with neutrinos, and applies regardless of whether the dark matter annihilation cross-section is s-wave or p-wave. To illustrate our bounds we apply them to a model of a supersymmetric neutralino annihilating to neutrinos, via a light mixed left-right handed sneutrino mediator. While this scenario was not constrained by previous data, the Planck limits on N-eff allow us to set a lower bound on the neutralino dark matter mass of 3.5 MeV.