Baryogenesis - Definition

Baryogenesis is the generic designation for the physical processes that generate matter (more specifically, a class of fundamental particle called baryon) from an otherwise matter-empty state (such as it is generally believed to be the state of the Universe at its onset, the so-called Big Bang).

The baryogenesis theories deal with different theories of physics to describe the possible mechanisms for generating baryons. They essentially incorporate the following areas:

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

Electroweak baryogenesis
GUT baryogenesis

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

Contents

1 Background

2 The Sakharov conditions

3 Matter content in the Universe

4 See also

4.1 Textbooks
4.2 Articles

Background

The Dirac equation was first announced by Paul Dirac around 1928, and it describes the dynamics of a single fermion. This equation predicts the existence of antiparticles as possible solutions, along with the expectable solutions for the corresponding particles. Nevertheless, this equation deals only with the dynamics of point-like, ½-spin charged particles such as the electron, saying nothing on the rate of production of either particles or anti-particles. In other words, the rate of production of electron might as well be the same as of the anti-electron (or positron). In principle, one concludes that in a situation of chemical ballance between the two, there would be (at best) very localized regions in space with more of either matter or anti-matter. This, however, is not enough to explain the amount of matter that survived the matter-formation era at the beginning of the Universe.

Prior to 1967, there were two main 'philosophical' interpretations to the state of the Universe right at its beginning: either there was already a small preference for matter, with the total baryonic number of the Universe different from zero (<math>B(time=0) \neq 0<math>); or, the Universe at its beginning was perfectly symmetric (<math>B(time=0) = 0<math>), 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 <math>B=0<math>. One challenge then is to explain how the Universe evolves to produce <math>B \neq 0<math>.

The Sakharov conditions

In 1967, Andrei Sakharov proposed a set of three conditions that a baryon-generating particle interaction to produce matter and anti-matter at different rates. These conditions were inspired in recent discoveries: the cosmic background radiation (Penzias and Wilson, 1965), and the CP-symmetry violation in the neutral kaon system (Cronin, Fitch and collaborators, 1964). The three conditions on a baryon-generating interaction are the following:

Baryon number <math>B<math> violation.
C-symmetry and CP-symmetry violation.
Withdrawal from thermal equilibrium.

The first condition may seem trivial, but to this day there is no experimental evidence on particle interactions where the baryon number is violated: so far, all observed particle interactions are so that the baryon number before and after such reactions is the same. Technically, this translates as the commutator of the baryon number quantum operator with the Standard Model hamiltonian operator is zero: <math>[B,H] = BH - HB = 0<math>. This is a strong indication that the Standard Model of Particle Physics is not a finalized theory, and other extensions to it are under active investigation. Among the possible extensions are Supersymmetry and Grand Unification Theories.

The second condition(s), however, has been known since the late 1950s and early 1960s. Violation of CP-symmetry is currently one important area of investigation in particle physics. This symmetry violation is related with the time inversion symmetry <math>T<math>, assuming that the CPT-symmetry is valid. In layman terms this translates into the rate of a given reaction is not the same if it evolved backwards in time.

The last condition involves Cosmology, and the usual frame for describing the Universe at its early stages in the form of the inflation theory. In essence, this condition states that the rate of a baryon-asymmetry generating reaction has to be lower than the rate of expansion of the Universe. In this situation, the particles and their corresponding anti-particles do not get the opportunity to achieve thermal equilibrium due to the fast expansion rate, and therefore the chances for catastrophic annihilation are reduced.

These three conditions have to occur at the same time in other to produce different contents of matter and anti-matter.

Matter content in the Universe

The challenges to the physics theories are then to explain how to produce this preference of matter over anti-matter, and also the size of this asymmetry. An important quantifier is the asymmetry parameter, <math>\eta = (n_B - n_{\bar B}) / n_\gamma<math>. This quantity relates the overall number density difference between baryons and anti-baryons (<math>n_B<math> and <math>n_{\bar B}<math>, respectively) and the number density of cosmic background radiation photon <math>n_\gamma<math>.

Observational results yield that <math>\eta<math> is approximately equal to <math>10^{-10}<math>. This means that for every 10 billion pairs of particle and anti-particle, there was one extra particle that was left without an anti-particle 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 (Cosmology) 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 (<math>1.25 \times 10^{11}<math>) galaxies. Assuming that they are, in average, similar to our own Galaxy, then each would contain around 100 billion suns (<math>10^{11}<math>). The weight of our Sun, which is a typical star, is around <math>2 \times 10^{30}<math> kilograms. Making the gross approximation that our Sun is composed of hydrogen, which weighs approximately <math>1.67 \times 10^{-27}<math> kilograms, then the last figure is equal to <math>1.2 \times 10^{57}<math> atoms (write the number 12 and then 56 zeros). The total number of atoms in the visible Universe is then approximately <math>1.5 \times 10^{79}<math>. For a Universe with 14 billion (<math>1.4 \times 10^{10}<math>) years of age, its spatial radius would be around <math>1.3 \times 10^{28}<math> centimeters, or a sphere of <math>9.2 \times 10^{84}<math> cubic centimeters. The atom density would then be around <math>1.6 \times 10^{-6}<math>. 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 kelvin, has a number density of 410 per cubic centimeter. The resulting estimation for the parameter <math>\eta<math> would then be approximately <math>4 \times 10^{-9}<math>. 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.