The annihilation of new dark matter candidates with masses m(X) in the MeV range may account for the galactic positrons that are required to explain the 511 keV gamma-ray flux from the galactic bulge. We study the impact of MeV-mass thermal relic particles on the primordial synthesis of H-2, He-4, and Li-7. If the new particles are in thermal equilibrium with neutrinos during the nucleosynthesis epoch they increase the helium mass fraction for m(X)less than or similar to10 MeV and are thus disfavored. If they couple primarily to the electromagnetic plasma they can have the opposite effect of lowering both helium and deuterium. For m(X)=4-10 MeV they can even improve the overall agreement between the predicted and observed H-2 and He-4 abundances.
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