Possible Evidence for the Existence of Antimatter on a Cosmological Scale in the Universe

We present some initial results of a detailed calculation of the cosmological $\gamma$-ray spectrum from matter-antimatter annihilation in the universe. The similarity of the calculated spectrum with the present observations of the $\gamma$-ray background spectrum above 1 MeV suggests that such observations may be evidence of the existence of antimatter on a large scale in the universe.