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| {{unsolved|physics|Why does the observable universe have more matter than antimatter?}}
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| {{Physical cosmology}}
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| In [[physical cosmology]], '''baryogenesis''' is the generic term for hypothetical physical processes that produced an [[symmetry|asymmetry]] between [[baryon]]s and antibaryons in the [[Big Bang|very early universe]], resulting in the substantial amounts of residual [[matter]] that make up the [[universe]] today.
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| Baryogenesis theories (the most important being electroweak baryogenesis and GUT baryogenesis) employ sub-disciplines of [[physics]] such as [[quantum field theory]], and [[statistical physics]], to describe such possible mechanisms. The fundamental difference between baryogenesis theories is the description of the interactions between fundamental particles.
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| The next step after baryogenesis is the much better understood [[Big Bang nucleosynthesis]], during which light [[atomic nuclei]] began to form.
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| == Background ==
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| The [[Dirac equation]],<ref name=Dirac1928>
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| {{cite journal
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| | author = [[Paul Dirac|P.A.M. Dirac]]
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| | year = 1928
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| | title = The Quantum Theory of the Electron
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| | journal = [[Proceedings of the Royal Society of London A]]
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| | volume = 117 | issue = 778 | pages = 610–624
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| | doi = 10.1098/rspa.1928.0023
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| |bibcode = 1928RSPSA.117..610D }}</ref> formulated by [[Paul Dirac]] around 1928 as part of the development of [[special relativity|relativistic]] [[quantum mechanics]], predicts the existence of [[antiparticle]]s along with the expected solutions for the corresponding particles. Since that time, it has been verified experimentally that every known kind of particle has a corresponding antiparticle. The [[CPT symmetry|CPT Theorem]] guarantees that a particle and its antiparticle have exactly the same mass and lifetime, and exactly opposite charge. Given this symmetry, it is puzzling that the universe does not have equal amounts of matter and [[antimatter]]. Indeed, there is no experimental evidence that there are any significant concentrations of antimatter in the observable universe.
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| There are two main interpretations for this disparity: either the universe began with a small preference for matter (total [[baryon number|baryonic number]] of the universe different from zero), or the universe was originally perfectly symmetric, but somehow a set of phenomena contributed to a small imbalance in favour of matter over time. The second point of view is preferred, although there is no clear experimental evidence indicating either of them to be the correct one.
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| == Sakharov conditions ==
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| In 1967, [[Andrei Sakharov]] proposed<ref name=Sakharov1967>
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| {{cite journal
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| | author = [[Andrei Sakharov|A. D. Sakharov]]
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| | year = 1967
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| | title = Violation of CP invariance, C asymmetry, and baryon asymmetry of the universe
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| | journal = [[Journal of Experimental and Theoretical Physics]]
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| | volume = 5 | pages = 24–27
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| | doi =
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| }}, republished as {{cite journal
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| | author = A. D. Sakharov
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| | year = 1991
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| | title = Violation of CP invariance, C asymmetry, and baryon asymmetry of the universe
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| | journal = [[Soviet Physics Uspekhi]]
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| | volume = 34 | pages = 392–393
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| | doi = 10.1070/PU1991v034n05ABEH002497
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| |bibcode = 1991SvPhU..34..392S
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| | issue = 5 }}</ref> a set of three necessary conditions that a [[baryon]]-generating interaction must satisfy to produce matter and antimatter at different rates. These conditions were inspired by the recent discoveries of the [[cosmic background radiation]]
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| <ref name=PenziasWilson1965>
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| {{cite journal
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| | author = [[Arno Allan Penzias|A. A. Penzias]] and [[Robert Woodrow Wilson|R. W. Wilson]]
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| | year = 1965
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| | title = A Measurement of Excess Antenna Temperature at 4080 Mc/s
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| | journal = [[Astrophysical Journal]]
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| | volume = 142 | pages = 419–421
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| | doi = 10.1086/148307
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| | bibcode=1965ApJ...142..419P
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| }}</ref> and [[CP-violation]] in the neutral [[kaon]] system.
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| <ref name=CroninFitch1964>
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| {{cite journal
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| | author = [[James Watson Cronin|J. W. Cronin]], [[Val Logsdon Fitch|V. L. Fitch]] ''et al.''
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| | year = 1964
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| | title = Evidence for the 2π decay of the {{PhysicsParticle|K|BR=2|TR=0}} meson
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| | journal = [[Physical Review Letters]]
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| | volume = 13 | pages = 138–140
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| | doi = 10.1103/PhysRevLett.13.138
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| | bibcode=1964PhRvL..13..138C
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| | issue = 4
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| }}</ref>
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| The three necessary "Sakharov conditions" are:
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| * [[Baryon number]] <math>B</math> violation.
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| * [[C-symmetry]] and [[CP-symmetry]] violation.
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| * Interactions out of [[thermal equilibrium]].
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| Baryon number violation is obviously a necessary condition to produce an excess of baryons over anti-baryons. But C-symmetry violation is also needed so that the interactions which produce more baryons than anti-baryons will not be counterbalanced by interactions which produce more anti-baryons than baryons.
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| CP-symmetry violation is similarly required because otherwise equal numbers of [[Chirality (physics)#Chirality and helicity|left-handed]] baryons and [[Chirality (physics)#Chirality and helicity)|right-handed]] anti-baryons would be produced, as well as equal numbers of left-handed anti-baryons and right-handed baryons.
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| Finally, the interactions must be out of thermal equilibrium, since otherwise [[CPT symmetry]] would assure compensation between processes increasing and decreasing the baryon number.<ref name=FarrarShaposhnikov1993>
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| {{cite journal
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| | author = M. E. Shaposhnikov, G. R. Farrar
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| | year = 1993
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| | title = Baryon Asymmetry of the Universe in the Minimal Standard Model
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| | journal = [[Physical Review Letters]]
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| | volume = 70 | pages = 2833–2836
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| | doi = 10.1103/PhysRevLett.70.2833
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| | arxiv = hep-ph/9305274
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| |bibcode = 1993PhRvL..70.2833F
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| | issue = 19 }}</ref>
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| Currently, there is no experimental evidence of particle interactions where the conservation of [[baryon number]] is broken [[Perturbation theory (quantum mechanics)|perturbatively]]: this would appear to suggest that all observed particle reactions have equal baryon number before and after. Mathematically, the [[commutator]] of the baryon number [[operator (mathematics)|quantum operator]] with the (perturbative) [[Standard Model]] [[hamiltonian (quantum mechanics)|hamiltonian]] is zero:
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| <math>[B,H] = BH - HB = 0</math>. However, the Standard Model is known to violate the conservation of baryon number non-perturbatively: a global U(1) anomaly.
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| Baryon number violation can also result from physics beyond the Standard Model (see [[supersymmetry]] and [[Grand unification theory|Grand Unification Theories]]).
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| The second condition – violation of [[CP-symmetry]] – was discovered in 1964 (direct CP-violation, that is violation of CP-symmetry in a decay process, was discovered later, in 1999). Due to [[CPT-symmetry]], violation of CP-symmetry demands violation of time inversion symmetry, or [[T-symmetry]].
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| In the out-of-equilibrium decay scenario,<ref name=Riotto99>
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| {{cite journal
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| | author = A. Riotto, M. Trodden
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| | year = 1999
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| | title = Recent progress in baryogenesis
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| | journal = [[Annual Review of Nuclear and Particle Science]]
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| | volume = 49 | pages = 46
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| | doi = 10.1146/annurev.nucl.49.1.35
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| |arxiv = hep-ph/9901362 |bibcode = 1999ARNPS..49...35R }}</ref> the last condition states that the rate of a reaction which generates baryon-asymmetry must be less than the rate of expansion of the universe. In this situation the particles and their corresponding antiparticles do not achieve thermal equilibrium due to rapid expansion decreasing the occurrence of pair-annihilation.
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| == Baryogenesis within the Standard Model ==
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| The [[Standard Model]] can incorporate baryogenesis, though the amount of net baryons (and leptons) thus created may not be sufficient to account for the present baryon asymmetry; this issue has not yet been determined decisively.
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| Baryogenesis within the Standard Model requires the [[Electroweak interaction|electroweak]] [[Higgs mechanism|symmetry breaking]] be a [[Phase transition#Ehrenfest classification|first-order]] [[phase transition]], since otherwise [[sphaleron]]s wipe off any baryon asymmetry that happened up to the phase transition, while later the amount of baryon non-conserving interactions is negligible.<ref name=KRS1985>
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| {{cite journal
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| | author = [[Vadim Kuzmin (physicist)|V. A. Kuzmin]], V. A. Rubakov, M. E. Shaposhnikov
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| | year = 1985
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| | title = On anomalous electroweak baryon-number non-conservation in the early universe
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| | journal = Physic Letters B
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| | volume = 155 | pages = 36–42
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| | doi = 10.1016/0370-2693(85)91028-7
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| |bibcode = 1985PhLB..155...36K }}</ref>
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| The [[phase transition]] [[Domain wall (string theory)|domain wall]] breaks the [[P-symmetry]] spontaneously, allowing for [[CP-symmetry]] violating interactions to create [[C-symmetry|C-asymmetry]] on both its sides: quarks tend to accumulate on the broken phase side of the domain wall, while anti-quarks tend to accumulate on its unbroken phase side. This happens as follows:<ref name="FarrarShaposhnikov1993"/>
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| Due to [[CP-symmetry]] violating [[electroweak]] interactions, some amplitudes involving quarks are not equal to the corresponding amplitudes involving anti-quarks, but rather have opposite phase (see [[CKM matrix]] and [[Kaon]]); since [[T-symmetry|time reversal]] takes an amplitude to its complex conjugate, [[CPT-symmetry]] is conserved.
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| Though some of their amplitudes have opposite phases, both quarks and anti-quarks have positive energy, and hence acquire the same phase as they move in space-time. This phase also depends on their mass, which is identical but depends both on [[flavor]] and on the [[Higgs field|Higgs]] [[Vacuum expectation value|VEV]] which changes along the domain wall. Thus certain sums of amplitudes for quarks have different absolute values compared to those of anti-quarks. In all, quarks and anti-quarks may have different reflection and transmission probabilities through the domain wall, and it turns out that more quarks coming from the unbroken phase are transmitted compared to anti-quarks.
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| Thus there is a net baryonic flux through the domain wall. Due to [[sphaleron]] transitions, which are abundant in the unbroken phase, the net anti-baryonic content of the unbroken phase is wiped off. However, sphalerons are rare enough in the broken phase as not to wipe off the excess of baryons there. In total, there is net creation of baryons.
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| In this scenario, non-perturbative electroweak interactions (i.e. the [[sphaleron]]) are responsible for the B-violation, the perturbative electroweak Lagrangian is responsible for the CP-violation, and the domain wall is responsible for the lack of thermal equilibrium; together with the CP-violation it also creates a C-violation in each of its sides.
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| == Matter content in the universe ==
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| {{see also|Baryon asymmetry}}
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| === Baryon asymmetry parameter ===
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| The challenges to the physics theories are then to explain ''how'' to produce this preference of matter over antimatter, and also the ''magnitude'' of this asymmetry. An important quantifier is the ''asymmetry parameter'',
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| :<math>\eta = \frac{n_B - n_{\bar B}}{n_\gamma}</math>. | |
| This quantity relates the overall number density difference between baryons and antibaryons
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| (n<sub>B</sub> and n<sub>{{overline|B}}</sub>, respectively)
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| and the number density of [[cosmic background radiation]] [[photon]]s n<sub>γ</sub>.
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| According to the Big Bang model, matter decoupled from the [[cosmic background radiation]] (CBR) at a temperature of roughly 3,000 [[kelvin]], corresponding to an average kinetic energy of {{val|fmt=commas|3000|u=K}} / ({{val|10.08|e=3|u=K/eV}}) = {{val|0.3|u=eV}}. After the decoupling, the ''total'' number of CBR photons remains constant. Therefore due to space-time expansion, the photon density decreases. The photon density at equilibrium temperature T per cubic centimeter, is given by
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| :<math>n_\gamma = \frac{1}{\pi^2} {\left(\frac{k_B T}{\hbar c}\right)}^3 \int_0^\infty \frac{x^2}{\exp(x) - 1} dx \simeq 20.3 \left(\frac{T}{1\text{K}}\right)^3 \text{cm}^{-3} </math>, | |
| with k<sub>B</sub> as the [[Boltzmann constant]], ħ as the [[Planck constant]] divided by 2π and c as the speed of light in vacuum.
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| At the current CBR photon temperature of {{val|2.725|u=K}}, this corresponds to a photon density n<sub>γ</sub> of around 411 CBR photons per cubic centimeter.
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| Therefore, the asymmetry parameter η, as defined above, is ''not'' the "good" parameter. Instead, the preferred asymmetry parameter uses the [[entropy]] density s,
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| :<math>\eta_s = \frac{n_B - n_{\bar B}}{s}</math>
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| because the entropy density of the universe remained reasonably constant throughout most of its evolution.
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| The entropy density is
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| :<math>s \ \stackrel{\mathrm{def}}{=}\ \frac{\mathrm{entropy}}{\mathrm{volume}} = \frac{p + \rho}{T} = \frac{2\pi^2}{45}g_{*}(T) T^3</math> | |
| with p and ρ as the pressure and density from the energy density tensor T<sub>μν</sub>, and g<sub>*</sub> as the effective number of degrees of freedom for "massless" particles (inasmuch as mc<sup>2</sup> ≪ k<sub>B</sub>T holds) at temperature T,
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| :<math>g_*(T) = \sum_\mathrm{i=bosons} g_i{\left(\frac{T_i}{T}\right)}^3 + \frac{7}{8}\sum_\mathrm{j=fermions} g_j{\left(\frac{T_j}{T}\right)}^3</math>, | |
| for bosons and fermions with g<sub>i</sub> and g<sub>j</sub> degrees of freedom at temperatures T<sub>i</sub> and T<sub>j</sub> respectively. At the present era, s = {{val|7.04|s=n<sub>γ</sub>}}.
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| == See also ==
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| * [[Lepton]]
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| * [[Leptogenesis (physics)|Leptogenesis]]
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| * [[CP violation]]
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| * [[Anthropic principle]]
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| * [[Affleck-Dine mechanism]]
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| * [[Timeline of the Big Bang]]
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| * [[Chronology of the universe]]
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| * [[Big Bang]]
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| == References ==
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| === Articles ===
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| {{reflist}}
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| === Textbooks ===
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| *{{cite book
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| | author = E. W. Kolb and M. S. Turner
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| | year = 1994
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| | title = The Early Universe
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| | publisher = [[Perseus Publishing]]
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| | isbn = 0-201-62674-8
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| }}
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| === Preprints ===
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| *{{cite arxiv
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| |author=A. D. Dolgov
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| |year=1997
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| |title=Baryogenesis, 30 Years After
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| |class=hep-ph
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| |eprint=hep-ph/9707419
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| }}
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| *{{cite arxiv
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| |author=A. Riotto
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| |year=1998
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| |title=Theories of Baryogenesis
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| |class=hep-ph/9807454
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| |eprint=hep-ph/9807454
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| }}
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| *{{cite journal
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| |author=M. Trodden
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| |year=1998
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| |title=Electroweak Baryogenesis
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| |doi=10.1103/RevModPhys.71.1463
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| |journal=Reviews of Modern Physics
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| |volume=71
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| |issue=5
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| |pages=1463
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| |arxiv=hep-ph/9803479
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| |bibcode = 1999RvMP...71.1463T }}
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| [[Category:Physical cosmology]]
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| [[Category:Particle physics]]
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| [[Category:Unsolved problems in physics]]
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| [[Category:Big Bang]]
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| {{Link GA|pl}}
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