The thermodynamics of the quark-hadron phase transition in the early universe

It is shown that a transition between quark matter and hadronic matter naturally occurs in the context of the early universe. The transition is realized by employing hard-core repulsive potentials (including the nucleon-nucleon interaction derived from a Yukawa potential and the π-π interaction derived from Weinberg's effective lagrangian) which vary linearly with density in the hadron phase and the QCD confining potential varying linearly with interquark separation in the quark phase. By comparing the free energies of the respective phases, a phase transition is shown; if first order, it occurs at ∼ 400 MeV corresponding to a hadron density of ∼ 13n₀. Given the uncertainties in the potentials used, it is found that the transition temperature must lie in the range 200-600 MeV with hadron densities ranging from 3-32n₀.