Number of Neutrino Families

Expansion of the Universe

This constraint follows from the fact that the expansion of the early Universe is dominated by the relativistic particles, the photons electrons, neutrinos, and their anti-particles. Suppose the Universe is made up of

photons + electron neutrinos + muon neutrinos

We can calculate how much energy is contained in the Universe. This will tell you how fast the Universe will expand. Next, suppose that the Universe is made up of

photons + electron neutrinos.

In this case, the amount of energy contained in the Universe is smaller and the Universe will expand more slowly. If there is another type of neutrino in addition to the electron, muon, and tau neutrinos, say the x-neutrino, then the energy contained in the Universe would be greater and the Universe would expand more quickly.

Expansion of the Universe and Big Bang Nucleosynthesis

How does the expansion rate of the Universe affect nucleosynthesis yields?

Recall that the production of helium, depends on the ratio of the neutrons and protons in the early Universe. At early times, when the Universe is dense and things get homogenized (are in equilibrium), we expect to get a well-defined number for the ratio of neutrons/protons which depends only on the temperature.

What determines the n/p ratio at the time of nucleosynthesis?

• As the Universe expands, interactions keep mixing the neutrons and protons making their ratio smaller as the Universe expands and cools. At a certain density and temperature the interaction rate becomes slow and the ratio neutron/proton freezes out. What we mean is that since there are no more interactions, the numbers of neutrons and protons stops changing. The helium abundance is thus determined by when this freeze-out occurs.

• If the Universe expands very quickly, the interactions can only keep up with the expansion of the Universe at early times and the neutron/proton ratio freezes-out at high temperatures and the ratio neutron/proton is large ===> high helium abundance.

• If the Universe expands very slowly, the weak interactions can keep up with the expansion for longer times (to lower temperature) and the freeze-out ratio of neutron/proton is small ===> small helium abundance.

Detailed calculations yield the following result on the number of neutrino families.

Big Bang nucleosynthesis, the helium abundance, and a reasonable range for the baryon density suggests that we have 3 types of neutrinos. Theory, in principle, does not predict this result. Work by experimental particle physicists using large accelerators have produced results consistent with this suggestion. In an odd sense, one could argue that the Terrestrial accelerator results confirm the existence of the Big Bang.