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We discuss a cosmological Friedmann model modified by inclusion of off-shell matter which has an equation of state p,\rho \propto T^5, p=1/4\rho . Such matter is shown to have energy density comparable with that of non-interacting radiation at temperatures of the order of the Hagedorn temperature, \sim 10^{12} K, indicating the possibility of a phase transition. It is argued that the T^5-phase, or an admixture, lies below the high-temperature T^4-phase
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