Can Dark Matter Annihilation Dominate the Extragalactic Gamma-Ray Background?

Annihilating dark matter (DM) has been discussed as a possible source of gamma-rays from the galactic center (GC) and contributing to the extragalactic gamma-ray background (EGB). Assuming universality of the density profile of DM halos, we show that it is quite unlikely that DM annihilation is a main constituent of EGB, without exceeding the observed gamma-ray flux from the GC. This argument becomes stronger when we include enhancement of the density profiles by supermassive black holes or baryon cooling. The presence of substructure may loosen the constraint, but only if a very large cross section as well as the rather flat profile are realized.