Analytic solutions for the energy density and the temperature of the QGP in the early Universe

Abstract

After the Big Bang and at a time estimated to be a millionth of a second, the Universe was in a phase that filledwith quark-gluon plasma. Due to the high temperature, the strong coupling constant that describes the strength of the strong forceacting on the quarks and the gluons, was so small. As a result, quarks and gluons inside the plasma behaved as an ideal gas ofgluons and massless quarks that weakly interact with each others. Hence, one can describe the characteristics of the plasma by theequations of states which relate energy density and pressure to its temperature as in the MIT bag model. Having these equations ofstates, one can solve Friedmann equations of the general relativity. In this work, we derive the analytic solutions for theFriedmann differential equations governing the time evolution of the energy density and the temperature of the quark-gluon plasmain that era of the early Universe adopting the MIT bag model.