“…Above 10 19 eV the universe becomes more and more transparent to photons and very high energy gamma rays can propagate a few tens of megaparsecs without losing a large amount of energy. As a result, these very high energy cosmogenic gamma-rays were discussed in the literature either as signatures of the so called Top-Down models (see for instance [166,167,168,169]) or as probes of UHECR acceleration in the local universe (e.g, [170,166,167,169,171,172,173,174,175,176,177,165]). Since electromagnetic cascades, piling up below 100 GeV, are produced during UHECR propagation and are likely to be associated with the production of cosmogenic neutrinos, it has been soon realized that measurements of the diffuse gamma-ray background could allow to put constraints on the cosmological evolution of the UHECR luminosity [23] and on the maximum allowable cosmogenic neutrino fluxes [178].…”