Extragalactic Inverse Compton Light from Dark Matter annihilation and the Pamela positron excess

We calculate the extragalactic diffuse emission originating from the up-scattering of cosmic microwave photons by energetic electrons and positrons produced in particle dark matter annihilation events at all redshifts and in all halos. We outline the observational constraints on this emission and we study its dependence on both the particle dark matter model (including the particle mass and its dominant annihilation final state) and on assumptions on structure formation and on the density profile of halos. We find that for low-mass dark matter models, data in the X-ray band provide the most stringent constraints, while the gamma-ray energy range probes models featuring large masses and pair-annihilation rates, and a hard spectrum for the injected electrons and positrons. Specifically, we point out that the all-redshift, all-halo inverse Compton emission from many dark matter models that might provide an explanation to the anomalous positron fraction measured by the Pamela payload severely overproduces the observed extragalactic gamma-ray background.