The Primordial Hot Plasma 115condensing into lepton and quark bound states. The forces binding them are in some
models calledtechnicolor forces.
Below the energy퐸≈1TeV we encounter the phase transition between exact and
spontaneously brokenSU( 2 )w⊗푈( 1 )퐵−퐿symmetry. The end of electroweak unifica-
tion is marked by the massification of the vector boson fields, the scalar Higgs fields
and the fermion fields.
One much discussed extension to the standard model issupersymmetry(SUSY).
This brings in a large number of new particles, some of which should be seen in this
temperature range. In this theory there is a conserved multiplicative quantum number,
R parity,definedby
푅=(− 1 )^3 퐵+퐿+^2 푠, (6.8)where퐵,퐿and푠are baryon number, lepton number and spin, respectively. All known
particles have푅=+1, but the theory allows an equal number of supersymmetric
partners,sparticles,having푅=−1. Conservation of푅ensures that SUSY sparticles
can only be produced pairwise, as sparticle–antisparticle pairs. The lightest sparticles
must therefore be stable, just as the lightest particles are.
One motivation for introducing this intermediate scale is thehierarchy problem:
why is푚Pso enormously much larger than푚W?Andwhyis푉Coulombso much larger
than푉Newton? SUSY has so many free parameters that it can ‘naturally’ explain these
problems.
Thermal Equilibrium. Motion of particles under electromagnetic interaction is
described by the Maxwell–Lorentz equations. The motion of a particle in a central
field of force퐹, as for instance an electron of charge푒moving at a distance푟around
an almost static proton, is approximated well by theCoulomb force
퐹=푒2
푟^2. (6.9)
Note that this has the same form as Newton’s law of gravitation, Equation (1.28). In
the electromagnetic case the strength of the interaction is푒^2 , whereas the strength
of the gravitational interaction isGM푚G.Thesetwocoupling constantsare expressed
in completely different units because they apply to systems of completely different
sizes. For the physics of radiation, the gravitational interaction can be completely
neglected but, for the dynamics of the expansion of the Universe, only the gravitational
interaction is important because celestial objects are electrically neutral.
The photons and the first particles which formed momentarily in the primordial
plasma were incessantly colliding and exchanging energy and momentum at relativis-
tic speeds. A few collisions were sufficient to distribute the available energy evenly
among them. Their reaction rates were much greater than the Hubble expansion rate,
so thermal equilibrium should have been maintained in any local comoving volume
element d푉.
There was no net inflow or outflow of energy, which defines the expansion as adi-
abaticadiabatic, as was done in Equation (5.25). The law of conservation of energy