126 Thermal History of the Universe
hadrons, forming a dense medium ofquark matter. Below the transition the quarks
become bound in hadronic matter, the separation between quarks in the nucleons
increases, and the interaction between any two quarks in a nucleon cease to interact
with quarks in neighboring nucleons. The degrees of freedom푔∗(푇)are then reduced
steeply to 69/4 as is shown in Figure 6.2 [1].
Quark matter may still exist today in the core of cold but dense stellar objects such
as neutron stars.
The color symmetrySU( 3 )cis valid and unbroken at this temperature, but it is in no
way apparent, because the hadrons are color-neutral singlets. The color force medi-
ated by gluons is also not apparent: a vestige of QCD from earlier epochs remains in
the form of strong interactions between hadrons. It appears that this force is mediated
by mesons, themselves quark bound states.
There is no trace of the weak symmetrySU( 2 )w, so the weak and electromagnetic
interactions look quite different. Their strengths are very different, and the masses
of the leptons are very different. Only the electromagnetic gauge symmetry푈( 1 )is
exactly valid, as is testified to by the conservation of electric charge.
All electrons and photons have an energy below the threshold for proton–
anti-proton production [see Equation (6.33)]. Then the number of protons, neutrons
and anti-nucleons will no longer increase as a result of thermal collisions, they can
only decrease.
We can follow the evolution of the function푔∗(푇)in Figure 6.2 [1]. Actually all the
particles in thermal equilibrium contribute, not only those accounted for in Equa-
tion (6.61), but also heavier particles which are thermalized by energetic photons and
pions in the tail of their respective Boltzmann distributions.
10050g*^20g*
g*S1055432
log T1 0 – 1 – 2Figure 6.2The evolution of the effective degrees of freedom contributing to the energy density,
푔∗(푇)and to the entropy density,푔∗S(푇), as functions of log푇, where the temperature is in units
of MeV [1].