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It is demonstrated that clusters of galaxies are able to keep cosmic rays for a time exceeding the age of the Universe. This phenomenon reveals itself by the production of the diffuse flux of high energy gamma and neutrino radiation due to the interaction of the cosmic rays with the intracluster gas. The produced flux is determined by the cosmological density of baryons, \b, if a large part of this density is provided by the intracluster gas. The signal from relic cosmic rays has to be compared with the flux produced by the late sources, which can be considered as a background in the search for cosmic ray production in the past. We calculate this flux considering the normal galaxies and AGN in the clusters as the sources of cosmic rays. Another potential cosmic ray source is the shock in the gas accreting to a cluster. We found that this background is relatively high: the diffuse fluxes produced by relic cosmic rays are of the same order of magnitude which can be expected from AGN in the clusters. In all cases the predicted diffuse gamma-ray flux is smaller than the observed one and the diffuse neutrino flux can be seen as the small bump at E\ 10⁶ GeV over the atmospheric neutrino flux. A bright phase in the galaxy evolution can be a source of the relic cosmic rays in clusters, revealing itself by diffuse gamma and neutrino radiations. We found that the observation of a signal from the bright phase is better for an individual cluster.
Berezinsky et al. (Wed,) studied this question.