One of the most striking facts about the universe is the paucity of antimatter compared to matter. There is ample evidence for this. For example, cosmic rays are overwhelmingly composed of matter and what little antimatter is present is compatible with its production in intergalactic collisions of matter with photons. Neither do we see intense outbursts of electromagnetic radiation that would accompany the annihilation of clouds of matter with similar clouds of antimatter. The absence of antimatter is very puzzling, because in the original Big Bang it would be natural to assume a total baryon number B = 0.17 Assuming that baryon number is conserved, then during the period when kT was large compared to hadron energies, baryons and antibaryons would be in equilibrium with photons via reversible reactions such as

 

 

and the number densities of protons and antiprotons would be comparable with the photon number density. This situation would continue until the temperature fell to a point where the photons no longer had sufficient energy to produce pp pairs. Protons and antiprotons would then annihilate each other until the expansion had proceeded to a point where the density of protons and antiprotons was such that mutual annihilation became increasingly unlikely. The critical temperature is kT ≈ 20 MeV and at this point the ratios of baryons and antibaryons to photons "freezes" to values that can be calculated to be

 

 

with of course N_B' /N_B = 1. These ratios would then be maintained in time, whereas the ratios currently observed are

 

 

so that the prediction (2) fails spectacularly. However, in the equilibrium state the numbers of protons and antiprotons was so large that it would require only a very small excess of protons over antiprotons – about one in 10⁹ – to have developed since the initial Big Bang for (2) and (3) to be reconciled.

 

The conditions whereby a baryon-antibaryon asymmetry could arise were first stated by Sakharov. It is necessary to have: (a) an interaction that violates charge conjugation C and the combined symmetry CP; (b) an interaction that violates baryon number; and (c) a non-equilibrium situation must exist at some point to seed the process. The reason for the first condition is that a baryon excess cannot be generated if the production of any particular particle (e.g. the proton) is balanced by an equal production of the corresponding antiparticle (the antiproton), as required by C or CP conservation. Baryon number violation is also obviously necessary and seems at first to be incompatible with the standard model in which, under present conditions, baryon number is conserved and the symmetry breaking between the electromagnetic and weak interactions is characterized by an energy scale of order 100 GeV. However, immediately after the Big Bang, thermal energies were very large compared to the energy scale of electroweak symmetry breaking and, if current theory is correct, the universe underwent a phase transition about 10^–7 s after the Big Bang from a state in which the electroweak symmetry was fully realized to the present state in which it is badly broken. Furthermore, it can be shown that during this transition, in which the universe was in a non-equilibrium state, satisfying requirement (c), sufficient baryon number violations occurred to enable the observed matter–antimatter asymmetry to be understood, provided there is sufficient C and CP violation. Unfortunately, while both C and CP violation occur in the standard model, the CP violation is much too small to explain the observed asymmetry. In contrast, supersymmetric theories, with their host of new particles, contain several unknown mixing angles and CP-violating phases, and by adjusting these parameters it is possible to induce much larger CP-violating effects than those predicted in the standard model. However, until these, or CP-violating effects from some other source `beyond the standard model' are experimentally detected, the origin of the matter–antimatter asymmetry in the universe remains an unsolved problem.