We discuss a cosmological Friedmann model modified by inclusion of off-shell
matter which has an equation of state p,ρ∝T5,p=1/4ρ. Such
matter is shown to have energy density comparable with that of non-interacting
radiation at temperatures of the order of the Hagedorn temperature, ∼1012 K, indicating the possibility of a phase transition. It is argued that
the T5-phase, or an admixture, lies below the high-temperature T4-phase