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Baryogenesis is the generic designation for the hypothetical physical processes that generated an asymmetry between baryons and anti-baryons in the very early universe.

Baryogenesis theories deal with different sub-fields of physics to describe the possible mechanisms for generating baryons. Most important are:

The fundamental difference between baryogenesis theories is the description of the interactions between fundamental particles. Among the baryogenesis theories are:

The next step after baryogenesis, is the much better understood nucleosynthesis, the forming of atomic nuclei.

Background

The Dirac equation, formulated by Paul Dirac around 1928 as part of the development of relativistic quantum mechanics, predicts the existence of antiparticles along with the expected solutions for the corresponding particles. Since that time, it has been verified experimentally that every particle has a corresponding antiparticle. The CPT Theorem guarantees that a particle and its anti-particle 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.

There are two main interpretations for this disparity: either when the universe began there was already a small preference for matter, with the total baryonic number of the universe different from zero ( $B(time=0)\neq 0$ ); or, the universe was originally perfectly symmetric ( $B(time=0)=0$ ), but somehow a set of phenomena contributed to a small unbalance. The second point of view is preferred, although there is no clear experimental evidence indicating either of them to be the correct one. The aforementioned preference is merely based on the following philosophical 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 the baryonic number $B=0$ . One challenge then is to explain how the universe evolves to produce $B\neq 0$ .

The Sakharov conditions

In 1967, Andrei Sakharov proposed 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 (Penzias and Wilson, 1965) and CP-violation in the neutral kaon system (Cronin, Fitch and collaborators, 1964). The three necessary "Sakharov conditions" are:

Baryon number $B$ violation.
C-symmetry and CP-symmetry violation.
Withdrawal from thermal equilibrium.

Currently, there is no experimental evidence of particle interactions where the baryon number is violated: all observed particle reactions have equal baryon number before and after. Mathematically, the commutator of the baryon number quantum operator with the Standard Model hamiltonian is zero: $[B,H]=BH-HB=0$ . This suggests physics beyond the Standard Model (see supersymmetry and Grand Unification Theories).

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). If CPT-symmetry is assumed, violation of CP-symmetry demands violation of time inversion symmetry, or T-symmetry.

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.

Matter content in the universe

The 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 size of this asymmetry. An important quantifier is the asymmetry parameter,

\eta ={\frac {n_{B}-n_{\bar {B}}}{n_{\gamma }}}

.

This quantity relates the overall number density difference between baryons and anti-baryons ( $n_{B}$ and $n_{\bar {B}}$ , respectively) and the number density of cosmic background radiation photon $n_{\gamma }$ . Because baryon number violating particle interactions have not yet been observed in the energy ranges obtained in laboratory, it is assumed that, after the Big Bang, no baryogenesis occurs explicitly, wherefore the asymmetry should not change.

According to the Big Bang model, matter decoupled from the cosmic background radiation (CBR) at a temperature of roughly 3000 kelvins, corresponding to an average kinetic energy of $3000\ \mathrm {K} /(10.08\times 10^{4}\ \mathrm {K/eV} )=0.3\ \mathrm {eV}$ . 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 kelvin and per cubic centimeter, is given by: $n_{\gamma }={\frac {1}{\pi ^{2}}}{\left({\frac {k_{B}T}{\hbar c}}\right)}^{3}\int _{0}^{\infty }{\frac {x^{2}}{\exp ^{x}-1}}dx\simeq 20.3T^{3}$ , with $k_{B}$ as the Boltzmann constant, $\hbar$ as the Planck constant divided by $2\pi$ and $c$ as the speed of light in vacuum. In the numeric approximation at the left hand side of the equation, the convention $c=\hbar =k_{B}=1$ was used (natural units), and for T in kelvins the result is given in K^-3 cm^-3. At the current CBR photon temperature of T = 2.73 K, this corresponds to a photon density $n_{\gamma }$ 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 entropy density s,

\eta _{s}={\frac {n_{B}-n_{\bar {B}}}{s}}

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

s\equiv {\frac {\mathrm {entropy} }{\mathrm {volume} }}={\frac {p+\rho }{T}}={\frac {2\pi ^{2}}{45}}g_{*}(T)T^{3}

with $p$ and $\rho$ as the pressure and density from the energy density tensor $T_{\mu \nu }$ , and $g_{*}$ as the effective number of degrees of freedom for "massless" ( $mc^{2}<\!\!<k_{B}T$ ) particles, at temperature $T$ ,

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}

,

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, $s=7.04n_{\gamma }$ .

A naive estimation of the baryon asymmetry of the universe

Observational results yield that η is approximately equal to 10⁻¹⁰ — more precisely, 2.6 < η × 10¹⁰ < 6.2. This means that for every 10 billion pairs of particle and antiparticle, there was one extra particle that was left without an antiparticle with which to annihilate into background radiation. This is a very small number, and explaining how to obtain it is very difficult: one is trying to make predictions to the very large (large-scale structure of the cosmos) based on the laws of the very small (particle physics)!

A reasonable idea of how this number is found experimentally follows. The Hubble Space Telescope surveys report that the observable universe contains approximately 125 billion (1.25×10¹¹) galaxies. Assuming that they are, in average, similar to our own galaxy, each contains around 100 billion (10¹¹) stars. The mass of the Sun, which is a typical star, is around 2×10³⁰ kg. Making the approximation that our Sun is composed only of hydrogen atoms, each of which weighs approximately 1.67×10⁻²⁷ kg, the Sun contains 1.2×10⁵⁷ atoms. The total number of atoms in the observable universe is then approximately 1.5×10⁷⁹. The universe is 14 billion (1.4×10¹⁰) years old, so the farthest away we can see is 14 billion light years, or 1.3×10²⁶ m. This means that the observable universe is a sphere of 9.7×10⁷⁸ m³. The atom density would then be around 1.6 m⁻³. On the other hand, statistical physics tells us that a gas of photons in thermal equilibrium at the temperature of the cosmic background radiation, 2.73 K, has a number density of 4.1×10⁸ m⁻³. The resulting estimate of η is 4×10⁻⁹. This is not a bad approximation; it is only an order of magnitude above the value quoted in the literature. The exact experimental value involves measuring the concentration of chemical elements in the universe not originating from stellar synthesis.

Philosophical considerations

It should be noted that, were there not a disparity between baryons and anti-baryons of the kind observed, it is questionable whether in fact there would be matter which would allow life capable of observing it.

This is a common argument presented in answer to issues of "why is the universe as it is", and in essence, answers the question by saying that in those universes or visible sections of the cosmos which did not have conditions favorable for life, no life would have emerged to notice it. If an asymmetry between baryons and anti-baryons was an essential prerequisite for the material existence of stars, planets and life, then (the argument goes) there may have been countless universes or sections of the cosmos in which life could not emerge, until a section in which the appropriate asymmetries came about eventually by chance, in which observers could exist. These observers would then notice the conditions, however atypical, which allowed their existence.

Similar arguments are also considered by some scientists, when answering the question why our planet within the cosmos is as it is, or why does life exist on earth.

External links

hep-ph/9707419 A. D. Dolgov, Baryogenesis, 30 years after.
hep-ph/9807454 A. Riotto, Theories of baryogenesis. CERN preprint CERN-TH/98-204.
hep-ph/9803479 M. Trodden, Electroweak baryogenesis.

@@ Line 30: / Line 30: @@
 This suggests physics beyond the Standard Model (see [[supersymmetry]] and [[GUT|Grand Unification Theories]]).
-The second condition &mdash; violation of [[CP-symmetry]] &mdash; was discovered in 1964 (direct CP-volation was discovered later, in 2001). If [[CPT-symmetry]] is assumed, violation of CP-symmetry demands violation of time inversion symmetry, or [[T-symmetry]].
+The second condition &mdash; violation of [[CP-symmetry]] &mdash; was discovered in 1964 (direct CP-violation, that is violation of CP-symmetry in a decay process, was discovered later, in 1999). If [[CPT-symmetry]] is assumed, violation of CP-symmetry demands violation of time inversion symmetry, or [[T-symmetry]].
 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.