Baryogenesis

• The universe around us consists mostly of matter. Anti-matter (anti-protons, anti-neutrons, positrons) is very rare.
• In Big Bang theory particles and antiparticles exist in equal numbers in the thermal equilibrium of the early universe. Then they annihilate by pairs, and at the end there are equal numbers of particles and anti-particles. Thus, the universe should be filled with the same amount of matter as anti-matter.

This is know as the baryon problem. Somehow the universe managed to create more matter than anti-matter. The process of creating more matter at the expense of anti-matter is called baryogenesis.

The solution to the baryogenesis problem lies in the assumption of thermal equilibrium. If the universe was in thermal equilibrium all the time, there is no way there can be excess of matter over anti-matter.

Fortunately, there are two moments in the history of the universe when it was not in thermal equilibrium: during GUT and electroweak phase transitions. The phase transition is a non-equilibrium process.

Cosmologists think that during one of those two phase transitions the excess of matter was produced. This excess is very small, one part in one billion, but it is enough to shape the universe as it is.

The problem is baryogenesis is largely unsolved, we even do not know which of the two phase transitions was responsible for it.

Nucleosynthesis

Shortly after electron - positron pairs annihilated at 10¹⁰ K (the universe is about 1 second old), helium and trace amounts of other isotopes were synthesized (the universe is about 100 seconds old).

• Protons and neutrons combine to form D (²H).
• Deuterium captures a proton and becomes ³He, or
• Deuterium captures a neutron and becomes ³H (ultra-heavy hydrogen).
• ³He captures a neutron to become ⁴He (normal helium), or
• ³H captures a proton to become ⁴He.
• ⁴He captures ³H to become ⁷Li, or
• ⁴He captures ³He and emits one electron to become ⁷Li.

About 25% of all protons and neutrons combined to form He.

Within a small region of the universe there were 100 protons and neutrons just before the nucleosynthesis. During the nucleosynthesis, 24% of all baryons turned into helium. How many helium nuclei were made in this region of space?

A.

1

B.

6

C.

24

D.

100

An unexpected side result

It turns out that the precise amount of helium produced depends on how many different neutrino species are there. The modern particle physics predicts that there should be three different neutrino species in the universe. Using the Big Bang nucleosynthesis, we can measure this number

$$2.2 < N_\nu < 3.2.$$

And it is consistent with the theory.

Can $N_\nu$ be not integer?