Astroparticle Physics

210 9 The Early Universebaryon-number-violatingprocessesviolationof C and CP symmetrydeparturefrom thermal equilibriumSakharov conditionsquantum anomaliesincompletenessof the Standard Model1. baryon-number-violating processes;2. violation of C and CP symmetry;3. departure from thermal equilibrium.The first condition must clearly hold, or else a universewith B = 0 will forever have B = 0. In the second condition,C refers to charge conjugation and P to parity. C andCP symmetry roughly means that a system of particles behavesthe same as the corresponding system made of antiparticles.If all matter and antimatter reactions proceed atthe same rate, then no net baryon number develops; thus,violation of C and CP symmetry is needed. The third conditionon departure from equilibrium is necessary in order toobtain unequal occupation of particle and antiparticle states,which necessarily have the same energy levels.A given theory of the early universe that satisfies atsome level the Sakharov conditions will in principle predicta baryon density or, equivalently, a baryon-to-photonratio η.One wants the net baryon number to be consistent with themeasured baryon-to-photon ratio η = n b /n γ ≈ 5×10 −10 .Itis not entirely clear how this can be satisfied, and a detaileddiscussion goes beyond the scope of this book. Here onlysome of the currently favoured ideas will be mentioned.Baryon-number violation is predicted by Grand UnifiedTheories, but it is difficult there to understand how the resultingbaryon density could be preserved when this is combinedwith other ingredients such as inflation. Surprisingly,a non-zero baryon number is also predicted by quantumanomalies 2 in the usual Standard Model, and this is cur-rently a leading candidate for baryogenesis.CP violation is observed in decays of K and B mesonsand it is predicted by the Standard Model of particle physicsbut at a level far too small to be responsible for baryogenesis.If nature includes further CP-violating mechanisms from additionalHiggs fields, as would be present in supersymmetricmodels, then the effect could be large enough to account forthe observed baryon density. This is one of the clearest indicationsfrom cosmology that the Standard Model is incompleteand that other particles and interactions must exist. Ithas been an important motivating factor in the experimental2 Quantum anomalies can arise if a classical symmetry is brokenin the process of quantization and renormalization. The perturbativetreatment of quantum field theories requires a renormalization,and this adds non-invariant counter terms to the invariantLagrange density that one gets at the classical level.