  Over the past few decades, an anomalous 511 keV gamma-ray line has been
observed from the centre of the Milky Way. Dark matter (DM) in the form of
light weakly interacting massive particles (WIMPs) annihilating into
electron-positron pairs has been one of the leading hypotheses of the observed
emission. Given the small required cross section, a further coupling to lighter
particles is required to produce the correct relic density. Here, we derive
constraints from the Planck satellite on light WIMPs that were in equilibrium
with either the neutrino or electron sector in the early universe. For the
neutrino sector, we obtain a lower bound on the WIMP mass of 4 MeV for a real
scalar and 10 MeV for a Dirac fermion DM particle, at 95% CL. For the electron
sector, we find even stronger bounds of 7 and 11 MeV, respectively. Using these
results, we show that, in the absence of additional ingredients such as dark
radiation, the light thermally produced WIMP explanation of the 511 keV excess
is strongly disfavoured by the latest cosmological data. This suggests an
unknown astrophysical or more exotic DM source of the signal.
