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We calculate the extragalactic diffuse emission originating from theup-scattering of cosmic microwave photons by energetic electrons and positronsproduced in particle dark matter annihilation events at all redshifts and inall halos. We outline the observational constraints on this emission and westudy its dependence on both the particle dark matter model (including theparticle mass and its dominant annihilation final state) and on assumptions onstructure formation and on the density profile of halos. We find that forlow-mass dark matter models, data in the X-ray band provide the most stringentconstraints, while the gamma-ray energy range probes models featuring largemasses and pair-annihilation rates, and a hard spectrum for the injectedelectrons and positrons. Specifically, we point out that the all-redshift,all-halo inverse Compton emission from many dark matter models that mightprovide an explanation to the anomalous positron fraction measured by thePamela payload severely overproduces the observed extragalactic gamma-raybackground.

Extragalactic Inverse Compton Light from Dark Matter Annihilation and the Pamela Positron Excess