In

physical cosmologyPhysical cosmology, as a branch of astronomy, is the study of the largest-scale structures and dynamics of the universe and is concerned with fundamental questions about its formation and evolution. For most of human history, it was a branch of metaphysics and religion...

,

**baryogenesis** is the generic term for hypothetical physical processes that produced an

asymmetrySymmetry generally conveys two primary meanings. The first is an imprecise sense of harmonious or aesthetically pleasing proportionality and balance; such that it reflects beauty or perfection...

between

baryonA baryon is a composite particle made up of three quarks . Baryons and mesons belong to the hadron family, which are the quark-based particles...

s and antibaryons in the

very early universeThe Big Bang theory is the prevailing cosmological model that explains the early development of the Universe. According to the Big Bang theory, the Universe was once in an extremely hot and dense state which expanded rapidly. This rapid expansion caused the young Universe to cool and resulted in...

, resulting in the substantial amounts of residual

matterMatter is a general term for the substance of which all physical objects consist. Typically, matter includes atoms and other particles which have mass. A common way of defining matter is as anything that has mass and occupies volume...

that make up the

universeThe Universe is commonly defined as the totality of everything that exists, including all matter and energy, the planets, stars, galaxies, and the contents of intergalactic space. Definitions and usage vary and similar terms include the cosmos, the world and nature...

today.

Baryogenesis theories (the most important being electroweak baryogenesis and GUT baryogenesis) employ sub-disciplines of

physicsPhysics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...

such as

quantum field theoryQuantum field theory provides a theoretical framework for constructing quantum mechanical models of systems classically parametrized by an infinite number of dynamical degrees of freedom, that is, fields and many-body systems. It is the natural and quantitative language of particle physics and...

, and

statistical physicsStatistical physics is the branch of physics that uses methods of probability theory and statistics, and particularly the mathematical tools for dealing with large populations and approximations, in solving physical problems. It can describe a wide variety of fields with an inherently stochastic...

, to describe such possible mechanisms. The fundamental difference between baryogenesis theories is the description of the interactions between fundamental particles.

The next step after baryogenesis is the much better understood

Big Bang nucleosynthesisIn physical cosmology, Big Bang nucleosynthesis refers to the production of nuclei other than those of H-1 during the early phases of the universe...

, during which light atomic nuclei began to form.

## Background

The

Dirac equationThe Dirac equation is a relativistic quantum mechanical wave equation formulated by British physicist Paul Dirac in 1928. It provided a description of elementary spin-½ particles, such as electrons, consistent with both the principles of quantum mechanics and the theory of special relativity, and...

, formulated by

Paul DiracPaul Adrien Maurice Dirac, OM, FRS was an English theoretical physicist who made fundamental contributions to the early development of both quantum mechanics and quantum electrodynamics...

around 1928 as part of the development of

relativisticSpecial relativity is the physical theory of measurement in an inertial frame of reference proposed in 1905 by Albert Einstein in the paper "On the Electrodynamics of Moving Bodies".It generalizes Galileo's...

quantum mechanicsQuantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...

, predicts the existence of

antiparticleCorresponding to most kinds of particles, there is an associated antiparticle with the same mass and opposite electric charge. For example, the antiparticle of the electron is the positively charged antielectron, or positron, which is produced naturally in certain types of radioactive decay.The...

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 TheoremCPT symmetry is a fundamental symmetry of physical laws under transformations that involve the inversions of charge, parity, and time simultaneously.-History:...

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

antimatterIn particle physics, antimatter is the extension of the concept of the antiparticle to matter, where antimatter is composed of antiparticles in the same way that normal matter is composed of particles...

. Indeed, there is no experimental evidence that there are any significant concentrations of antimatter in the observable universe.

There are two main interpretations for this disparity: either the universe began with a small preference for matter (total

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. The preference is based on the following point of view: if the universe encompasses everything (time, space, and matter),

*nothing* exists outside of it and therefore

*nothing* existed before it, leading to a total baryonic number of 0. From a more scientific point of view, there are reasons to expect that any

*initial* asymmetry would be wiped out to zero during the early history of the universe. One challenge then is to explain how the total baryonic number is not conserved.

## Sakharov conditions

In 1967,

Andrei SakharovAndrei Dmitrievich Sakharov was a Soviet nuclear physicist, dissident and human rights activist. He earned renown as the designer of the Soviet Union's Third Idea, a codename for Soviet development of thermonuclear weapons. Sakharov was an advocate of civil liberties and civil reforms in the...

proposed a set of three necessary conditions that a

baryonA baryon is a composite particle made up of three quarks . Baryons and mesons belong to the hadron family, which are the quark-based particles...

-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

and CP-violation in the neutral

kaonIn particle physics, a kaon is any one of a group of four mesons distinguished by the fact that they carry a quantum number called strangeness...

system.

The three necessary "Sakharov conditions" are:

- Baryon number violation.
- C-symmetry
In physics, C-symmetry means the symmetry of physical laws under a charge-conjugation transformation. Electromagnetism, gravity and the strong interaction all obey C-symmetry, but weak interactions violate C-symmetry.-Charge reversal in electromagnetism:...

and CP-symmetry violation.
- Interactions out of thermal equilibrium
Thermal equilibrium is a theoretical physical concept, used especially in theoretical texts, that means that all temperatures of interest are unchanging in time and uniform in space...

.

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.

CP-symmetry violation is similarly required because otherwise equal numbers of left-handed baryons and right-handed anti-baryons would be produced, as well as equal numbers of left-handed anti-baryons and right-handed baryons.

Finally, the interactions must be out of thermal equilibrium, since otherwise

CPT symmetryCPT symmetry is a fundamental symmetry of physical laws under transformations that involve the inversions of charge, parity, and time simultaneously.-History:...

would assure compensation between processes increasing and decreasing the baryon number.

Currently, there is no experimental evidence of particle interactions where the conservation of

baryon number is broken

perturbativelyIn quantum mechanics, perturbation theory is a set of approximation schemes directly related to mathematical perturbation for describing a complicated quantum system in terms of a simpler one. The idea is to start with a simple system for which a mathematical solution is known, and add an...

: this would appear to suggest that all observed particle reactions have equal baryon number before and after. Mathematically, the

commutatorIn mathematics, the commutator gives an indication of the extent to which a certain binary operation fails to be commutative. There are different definitions used in group theory and ring theory.-Group theory:...

of the baryon number quantum operator with the (perturbative)

Standard ModelThe Standard Model of particle physics is a theory concerning the electromagnetic, weak, and strong nuclear interactions, which mediate the dynamics of the known subatomic particles. Developed throughout the mid to late 20th century, the current formulation was finalized in the mid 1970s upon...

hamiltonianIn quantum mechanics, the Hamiltonian H, also Ȟ or Ĥ, is the operator corresponding to the total energy of the system. Its spectrum is the set of possible outcomes when one measures the total energy of a system...

is zero:

. However, the Standard Model is known to violate the conservation of baryon number non-perturbatively: a global U(1) anomaly.

Baryon number violation can also result from physics beyond the Standard Model (see

supersymmetryIn particle physics, supersymmetry is a symmetry that relates elementary particles of one spin to other particles that differ by half a unit of spin and are known as superpartners...

and

Grand Unification TheoriesThe term Grand Unified Theory, often abbreviated as GUT, refers to any of several similar candidate models in particle physics in which at high-energy, the three gauge interactions of the Standard Model which define the electromagnetic, weak, and strong interactions, are merged into one single...

).

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-symmetryT Symmetry is the symmetry of physical laws under a time reversal transformation: T: t \mapsto -t.Although in restricted contexts one may find this symmetry, the observable universe itself does not show symmetry under time reversal, primarily due to the second law of thermodynamics.Time asymmetries...

.

In the out-of-equilibrium decay scenario, 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.

## Baryogenesis within the Standard ModelThe Standard Model of particle physics is a theory concerning the electromagnetic, weak, and strong nuclear interactions, which mediate the dynamics of the known subatomic particles. Developed throughout the mid to late 20th century, the current formulation was finalized in the mid 1970s upon...

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.

Baryogenesis within the Standard Model requires the

electroweakIn particle physics, the electroweak interaction is the unified description of two of the four known fundamental interactions of nature: electromagnetism and the weak interaction. Although these two forces appear very different at everyday low energies, the theory models them as two different...

symmetry breakingIn particle physics, the Higgs mechanism is the process in which gauge bosons in a gauge theory can acquire non-vanishing masses through absorption of Nambu-Goldstone bosons arising in spontaneous symmetry breaking....

be a first-order

phase transitionA phase transition is the transformation of a thermodynamic system from one phase or state of matter to another.A phase of a thermodynamic system and the states of matter have uniform physical properties....

, since otherwise

sphaleronA sphaleron is a static solution to the electroweak field equations of the Standard Model of particle physics, and it is involved in processes that violate baryon and lepton number. Such processes cannot be represented by Feynman diagrams, and are therefore called non-perturbative...

s wipe off any baryon assymetry that happened up to the phase transition, while later the amount of baryon non-conserving interactions is negligible.

The

phase transitionA phase transition is the transformation of a thermodynamic system from one phase or state of matter to another.A phase of a thermodynamic system and the states of matter have uniform physical properties....

domain wallA domain wall is a term used in physics which can have one of two distinct but similar meanings in magnetism, optics, or string theory. These phenomena can all be generically described as topological solitons which occur whenever a discrete symmetry is spontaneously broken.-Magnetism:In magnetism,...

breaks the P-symmetry spontaneously, allowing for CP-symmetry violating interactions to create

C-asymmetryIn physics, C-symmetry means the symmetry of physical laws under a charge-conjugation transformation. Electromagnetism, gravity and the strong interaction all obey C-symmetry, but weak interactions violate C-symmetry.-Charge reversal in electromagnetism:...

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:

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

KaonIn particle physics, a kaon is any one of a group of four mesons distinguished by the fact that they carry a quantum number called strangeness...

); since

time reversalT Symmetry is the symmetry of physical laws under a time reversal transformation: T: t \mapsto -t.Although in restricted contexts one may find this symmetry, the observable universe itself does not show symmetry under time reversal, primarily due to the second law of thermodynamics.Time asymmetries...

takes an amplitude to its complex conjugate, CPT-symmetry is conserved.

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

flavorFlavor or flavour is the sensory impression of a food or other substance, and is determined mainly by the chemical senses of taste and smell. The "trigeminal senses", which detect chemical irritants in the mouth and throat as well as temperature and texture, are also very important to the overall...

and on the

HiggsThe term Higgs appears in:* Alan Higgs, English businessman and philanthropist* Sir Derek Higgs, an English business leader and merchant banker* Eric Sidney Higgs, English archaeologist*Griffin Higgs...

VEVIn quantum field theory the vacuum expectation value of an operator is its average, expected value in the vacuum. The vacuum expectation value of an operator O is usually denoted by \langle O\rangle...

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.

Thus there is a net baryonic flux through the domain wall. Due to

sphaleronA sphaleron is a static solution to the electroweak field equations of the Standard Model of particle physics, and it is involved in processes that violate baryon and lepton number. Such processes cannot be represented by Feynman diagrams, and are therefore called non-perturbative...

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.

In this scenario, non-perturbative electroweak interactions (i.e. the

sphaleronA sphaleron is a static solution to the electroweak field equations of the Standard Model of particle physics, and it is involved in processes that violate baryon and lepton number. Such processes cannot be represented by Feynman diagrams, and are therefore called non-perturbative...

) 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.

### Baryon asymmetry parameter

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*,

.

This quantity relates the overall number density difference between baryons and antibaryons

(n

_{B} and n

_{}, respectively)

and the number density of cosmic background radiation

photonIn physics, a photon is an elementary particle, the quantum of the electromagnetic interaction and the basic unit of light and all other forms of electromagnetic radiation. It is also the force carrier for the electromagnetic force...

s n

_{γ}.

According to the Big Bang model, matter decoupled from the cosmic background radiation (CBR) at a temperature of roughly 3,000

kelvinThe kelvin is a unit of measurement for temperature. It is one of the seven base units in the International System of Units and is assigned the unit symbol K. The Kelvin scale is an absolute, thermodynamic temperature scale using as its null point absolute zero, the temperature at which all...

, corresponding to an average kinetic energy of / = . 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 kelvin and per cubic centimeter, is given by

,

with k

_{B} as the

Boltzmann constant, ħ as the

Planck constantThe Planck constant , also called Planck's constant, is a physical constant reflecting the sizes of energy quanta in quantum mechanics. It is named after Max Planck, one of the founders of quantum theory, who discovered it in 1899...

divided by 2π and c as the speed of light in vacuum.

At the current CBR photon temperature of , this corresponds to a photon density n

_{γ} of around 411 CBR photons per cubic centimeter.

Therefore, the asymmetry parameter η, as defined above, is

*not* the "good" parameter. Instead, the preferred asymmetry parameter uses the

entropyEntropy is a thermodynamic property that can be used to determine the energy available for useful work in a thermodynamic process, such as in energy conversion devices, engines, or machines. Such devices can only be driven by convertible energy, and have a theoretical maximum efficiency when...

density s,

because the entropy density of the universe remained reasonably constant throughout most of its evolution.

The entropy density is

with p and ρ as the pressure and density from the energy density tensor T

_{μν}, and g

_{*} as the effective number of degrees of freedom for "massless" particles (inasmuch as mc

^{2} ≪ k

_{B}T holds) at temperature T,

,

for bosons and fermions with g

_{i} and g

_{j} degrees of freedom at temperatures T

_{i} and T

_{j} respectively. At the present era, s = .

## See also

- Lepton
A lepton is an elementary particle and a fundamental constituent of matter. The best known of all leptons is the electron which governs nearly all of chemistry as it is found in atoms and is directly tied to all chemical properties. Two main classes of leptons exist: charged leptons , and neutral...

- Leptogenesis
In physical cosmology, leptogenesis is the generic term for hypothetical physical processes that produced an asymmetry between leptons and antileptons in the very early universe, resulting in the dominance of leptons over antileptons...

- CP violation
In particle physics, CP violation is a violation of the postulated CP-symmetry: the combination of C-symmetry and P-symmetry . CP-symmetry states that the laws of physics should be the same if a particle were interchanged with its antiparticle , and left and right were swapped...

- Anthropic principle
In astrophysics and cosmology, the anthropic principle is the philosophical argument that observations of the physical Universe must be compatible with the conscious life that observes it. Some proponents of the argument reason that it explains why the Universe has the age and the fundamental...

- Affleck-Dine mechanism