1. 1 Lecture-06 Baryogenesis Ping He ITP.CAS.CN 2006.04.21 http://power.itp.ac.cn/~hep/cosmology.htm

2. 2 6.1 Overview Grand unification (Grand unified theories – GUTs): to unify the strong, weak, and electromagnetic interactions and the quarks and leptons within the framework of a gauge field theory based upon a simple or semi-simple, non-Abelian symmetry group, e.g., SU(5), SO(10), E 6. GUTs predictions: (1) new interactions violate baryon number B and lepton L conservations, -- instability of the proton  proton decay; (2) large amount of superheavy magnetic monopoles. The B-violation interactions are extremely weak today, due to the longevity of proton. Standard model:

3. 3 Baryogenesis, based on these B-violation interactions: (1) can explain how the B-symmetry Universe can evolve into the B-asymmetry Universe; (2) can explain the present baryon-to-photon ratio; (3) can provide a mechanism to unify quarks and leptons. Predictions from baryogenesis based on GUTs conflicts with standard cosmology, that there are too much superheavy monopoles that are not observed.  inflation M: the energy scale of unification

4. 4 6.2 Evidence for a Baryon Asymmetry Anti-matter is rare on Earth, only in accelerator or cosmic ray. Also rare in the solar system, cosmic ray coming from the galaxy indicates that the galaxy is not anti-matter. On large scales: if matter and anti-matter co-exist, then there are strong   ray emission from nucleon-antinucleon annihilation. The absence of such   ray flux indicates the asymmetry of matter and anti-matter. In a locally-baryon-symmetric Universe nucleons and antinucleons remain in chemical equilibrium down to T ~ 22 MeV, when In order to avoid the “annihilation catastrophe” a physical mechanism should operate at T > 38 MeV, so that

5. 5 The most reasonable conclusion then is that the Universe at early times T>38MeV possessed an asymmetry between baryons and antibaryons which prevented the annihilation catastrophe. At high temperatures T>1GeV, thermal quark-antiquark pairs were present in great numbers,, so that the baryon asymmetry observed today corresponds to a tiny quark-antiquark asymmetry at early times ( ). Baryogenesis scenario provides a very attractive means by which this tiny asymmetry can arise from initially baryon symmetric Universe.

6. 6 3). In chemical equilibrium, the chemical potentials associated with all non-conserved quantum numbers vanish, that is, 6.3 The Basic Picture Three ingredients to generate non-zero baryon number from an initially baryon symmetric state, i.e., Sakharov Criteria: (1) Violation of Baryon number (B) symmetry; (2) Violation of C and CP symmetries; (3) A departure from thermal equilibrium. 1). It’s obviously. If baryon number is conserved in all interactions, the present baryon asymmetry can only reflect asymmetric initial conditions. 2). Without C and CP violation, B-nonconserving interactions will produce baryon and antibaryon excesses at the same rate  zero net baryon number. by CPT invariance, so, hence

7. 7 A toy model: to illustrate the mechanics of baryogenesis. Since the two final states have different baryon number,  B-nonconservation. If C and CP are violated, then. If a box containing equal numbers of bosons. symmetric initial conditions The mean net baryons produced by X is: produced by The mean net baryon number produced by a pair of X and decay is (C and CP violated)

8. 8  can be treated as indication of the degree of C and CP violation. When, can decay, but can also produce in pair in thermal collision, then: If always in thermal equilibrium, the process that produces baryon excess balance the one that perishes baryon  The asymmetry can be roughly estimated in the following way The correct way to do so should be handled by Boltzmann equation, which may have deviations of several orders of magnitude. when out-of-equilibrium ( ), due to B, C and CP violation, 

9. 9 6.4 Concluding Remarks (1) Sakharov Three Criteria, but notice the scenario of spontaneous baryogenesis; (2) The precise evolution of the baryon asymmetry is handled by Boltzmann Equation; (3) Lepton-genesis can be treated in a similar way; (4) The current GUTs are not successful.

10. 10 References E.W. Kolb & M.S. Turner, The Early Universe, Addison-Wesley Publishing Company, 1993 D. Bailin & A. Love, Cosmology in Gauge Field Theory and String Theory, IoP Publishing, 2004 俞允强，热大爆炸宇宙学，北京大学出版 社， 2001 范祖辉， Course Notes on Physical Cosmology, See this site.this site