Abstract
The strong cosmic microwave emission recently discovered plays an important role both in the X-ray emission by the inverse Compton effect and in the γ-ray absorption by pair creation. Since the mean free paths for these two processes are smaller than the cosmic radius, they take place successively in intergalactic space, thus forming a cascade shower. The cascade process results in an increase of the attenuation length of very high energy γ-rays in intergalactic space, and modifies the energy spectrum of electrons and γ-rays. However, the intergalactic space is found to be still opaque for γ-rays with energies greater than 1015 eV.

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