Cosmic neutrino background

The cosmic neutrino background is the part of the background radiation of the universe, which consists of neutrinos.

As the cosmic microwave background is the cosmic neutrino background, a remnant of the Big Bang, he goes back to the decoupling of neutrinos from the matter around two seconds after the Big Bang. The cosmic microwave background, however, was formed when the universe was about 380,000 years old. The cosmic neutrino background has today an estimated temperature of about 1.95 K. Since neutrinos with a low energy occur only very weakly interact with matter, they are extremely difficult to detect. However, there is compelling indirect evidence for its existence. The planned experiment to measure PTOLEMY has as a goal, the neutrino background directly.

Derivation of the temperature of the cosmic neutrino background

Substituting the temperature of the cosmic microwave background as given ahead, the temperature of the neutrino background can be estimated. Before the neutrinos decoupled from the rest of matter, the universe consisted mainly of neutrinos, electrons, positrons and photons, all of which were in thermal equilibrium with each other. As the temperature to about 2.5 MeV (see the article Natural units) fell, the neutrinos decoupled from the rest of matter. Despite this decoupling, the neutrinos had still the same temperature as the photons, when the universe still expanding. However, as the temperature fell below the electron mass, most of the electrons and positrons are extinguished by pair annihilation, whereby its energy and its entropy has been transferred to the photons, corresponding to an increase in the temperature of the photon gas. The ratio before and after the electron-positron pair annihilation of the temperature of the photons is thus the same as the ratio of the temperatures of the photons and neutrinos at the present background radiation. To determine this ratio, we assume that the entropy of the universe is obtained during the electron-positron pair annihilation approximation. with

Whereby the entropy of the actual number of degrees of freedom and the temperature call, we get

The temperature of the photon gas before and after the temperature of the electron-positron pair annihilation is. The factor is determined by the particle type:

• 2 for photons, since they are massless bosons,
• 2 * ( 7/8 ) for each of electrons and positrons as they are fermions.

Thus:

With today's value follows that.

The above consideration applies for massless neutrinos, which are always relativistic. For neutrinos with a non-zero rest mass of the approach over a temperature is not suitable, as they are non- relativistic. This happens when their thermal energy falls below the energy of their rest mass. In this case, the energy density should better be seen which is still well defined.

Indirect evidence for the cosmic neutrino background

Relativistic neutrinos contribute to the radiation density of the universe, which is usually expressed as a function of the effective number of neutrino generations:

The redshift call. The first term in square brackets describes the cosmic microwave background, the second the cosmic neutrino background. The Standard Model of elementary particle physics says with his three neutrino species requires the effective value.

Primordial nucleosynthesis

Since the effective number of neutrino species affects the expansion rate of the universe during the Big Bang Nucleosynthesis, the theoretically expected values ​​for the primordial abundances of light elements depend on her. Astrophysical measurements of the primordial abundances of helium -4 and deuterium lead to a value of at a confidence level of 68 %, which is consistent with the expectation from the standard model in line.

Anisotropies in the cosmic microwave background and structure formation

The presence of the cosmic neutrino background influenced both the development of anisotropies in the cosmic background radiation and the growth of density fluctuations in two ways: firstly by its contribution to the radiation density of the universe (which determines, for example, the time of transition from radiation- to matter-dominated universe ), on the other by the anisotropic pressure, which dampens the baryonic acoustic oscillations. Moreover suppress massive neutrinos which propagate freely, the structure formation on small length scales. From the five-year data acquisition of the satellite WMAP in combination with data on type I supernovae and information about the strength of the baryonic acoustic oscillations provide a value of at a confidence level of 68 %, which represents an independent confirmation of the barriers from the primordial nucleosynthesis. In the near future examinations such as the Planck Space Telescope is expected to reduce the current uncertainties by an order of magnitude.