The cosmic neutrino background (CNB, CνB) is the universe's background particle radiation composed of neutrinos. They are sometimes known as relic neutrinos.
Like the cosmic microwave background radiation (CMB), the CνB is a relic of the big bang, and while the CMB dates from when the universe was 379,000 years old, the CνB decoupled from matter when the universe was 2 seconds old. It is estimated that today the CνB has a temperature of roughly 1.95 K.
Since low-energy neutrinos interact only very weakly with matter, they
are notoriously difficult to detect and the CνB might never be observed
directly. There is, however, compelling indirect evidence for its existence.
Derivation of the temperature of the CνB
Given the temperature of the CMB, the temperature of the CνB can be estimated. Before neutrinos decoupled from the rest of matter, the universe primarily consisted of neutrinos, electrons, positrons, and photons, all in thermal equilibrium with each other. Once the temperature reached approximately 2.5 MeV,
the neutrinos decoupled from the rest of matter. Despite this
decoupling, neutrinos and photons remained at the same temperature as
the universe expanded. However, when the temperature dropped below the
mass of the electron, most electrons and positrons annihilated,
transferring their heat and entropy to photons, and thus increasing the
temperature of the photons. So the ratio of the temperature of the
photons before and after the electron-positron annihilation is the same
as the ratio of the temperature of the photons and the neutrinos today.
To find this ratio, we assume that the entropy of the universe was
approximately conserved by the electron-positron annihilation. Then
using
- ,
where σ is the entropy, g is the effective degrees of freedom and T is the temperature, we find that
- ,
where T
0 denotes the temperature before the electron-positron annihilation and T
1 denotes after. The factor g
0 is determined by the particle species:
0 denotes the temperature before the electron-positron annihilation and T
1 denotes after. The factor g
0 is determined by the particle species:
- 2 for photons, since they are massless bosons
- 2(7/8) each for electrons and positrons, since they are fermions
g
1 is just 2 for photons. So
1 is just 2 for photons. So
- .
The above discussion is valid for massless neutrinos, which are
always relativistic. For neutrinos with a non-zero rest mass, the
description in terms of a temperature is no longer appropriate after
they become non-relativistic; i.e., when their thermal energy 3/2 kT
ν falls below the rest mass energy m
νc2. Instead, in this case one should rather track their energy density, which remains well-defined.
ν falls below the rest mass energy m
νc2. Instead, in this case one should rather track their energy density, which remains well-defined.
http://en.wikipedia.org/wiki/Cosmic_neutrino_background
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