Cosmological consequences of permanent quark confinement

Summary

The Hagedorn model of hadronic matter was originally developed as an application of the bootstrap principle, but it is also a model which describes permanent quark confinement. Our remarkable prediction of the model is that hadronic matter cannot be heated beyond a finite maximum temperature (=T _q). In a cosmic context,T _q is the maximum temperature of the early universe; its existence follows simply by imposing the principle of permanent quark confinement. In the limitT →T _q, the Hagedorn model is ambiguous about the size of the early universe and about the numerical value of the hadronic energy density. However, once the temperature constraint is accepted, the uncertainty principle and the principle of permanent quark confinement require the absence of the essential singularity at cosmic timet = 0. This initial condition for the early universe may be interpreted as due to a strong, short-range repulsive core in the interaction between quark pairs (evident at the hadron level, for example, as a nucleon-nucleon hard core). The parameters of the (qq) hard core are calculated from known characteristics of the universe. The results are: for the range,R _qq≲0.07 fm; for the height, V₀ ≈ 4.6·10¹⁴ GeV. It then follows that the « big bang » was soft and started at t = 0 with temperatureT _q ≈ 1.6·10¹²K, radiusR _min ≈1/2·10¹³ cm and hadronic mass density ϱ_max ≈ 6·10¹⁶ gr/cm³.