Calculate the energy density versus temperature very early in the universe when the temperatures were above \(k T=300 \mathrm{MeV}\). At those temperatures, quarks and gluons were released from individual nuclei. Treat the quark-gluon plasma as a noninteracting relativistic gas. At those temperatures, the species that are in equilibrium with one other are: photons, the three neutrino species, electrons and positrons, muons and antimuons, up and down quarks and their antiparticles (all spin \(-\frac{1}{2}\) ), and spin-1 massless gluons. Like photons, the gluons are bosons, have two spin states each, and are their own antiparticle. There are eight varieties of gluons that change the three color states of the quarks. The strange, charm, top, and bottom quarks and tau leptons are heavier than \(300 \mathrm{MeV}\), so they do not contribute substantially at this temperature. Use your result and equation (9.1.1) to determine the temperature evolution as a function of the age of the universe during this era and its age when \(k T \approx 300 \mathrm{MeV}\).