The cosmic neutrino background (CNB or CnB[a]) is the universe's background particle radiation composed of neutrinos. They are sometimes known as relic neutrinos.
The CnB is a relic of the Big Bang; while the cosmic microwave background radiation (CMB) dates from when the universe was 379,000 years old, the CnB decoupled (separated) from matter when the universe was just one second old. It is estimated that today, the CnB has a temperature of roughly 1.95 K.
As neutrinos rarely interact with matter, these neutrinos still exist today. They have a very low energy, around 10−4 to 10−6 eV. Even high energy neutrinos are notoriously difficult to detect, and the CnB has energies around 1010 times smaller, so the CnB may not be directly observed in detail for many years, if at all. However, Big Bang cosmology makes many predictions about the CnB, and there is very strong indirect evidence that the CnB exists.
Given the temperature of the cosmic microwave background (CMB) the temperature of the cosmic neutrino background (CnB) can be estimated. It involves a change between two regimes:
At very high temperatures, 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 dropped to approximately 2.5 MeV (
17.4
×
10
9
{\displaystyle 17.4\times 10^{9}}
K), the neutrinos decoupled from the rest of matter, and for practical purposes, all lepton and photon interactions with these neutrinos stopped.[c]
Despite this decoupling, neutrinos and photons remained at the same temperature as the universe expanded as a "fossil" of the prior Regime 1, since both are cooled in the same way by the same process of cosmic expansion, from the same starting temperature. However, when the temperature dropped below double the mass of the electron, most electrons and positrons annihilated, transferring their heat and entropy to photons, 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 neutrinos and the photons in the current Regime 2. To find this ratio, we assume that the entropy s of the universe was approximately conserved by the electron-positron annihilation. Then using
where g is the effective number of degrees of freedom and T is the plasma or photon temperature. Once reactions cease, the entropy s should remain approximately "stuck" for all temperatures below the cut-off temperature, and we find that
Here
T
1
∝
T
n
{\displaystyle \;T_{1}\propto T_{\mathrm {\nu } }\;}
denotes the lowest temperature where pair production and annihilation were in equilibrium; and
T
2
∝
T
g
{\displaystyle \;T_{2}\propto T_{\mathrm {\gamma } }\;}
denotes the temperature after the temperature fell below the regime-shift temperature
T
1
{\displaystyle \;T_{1}\;}
, after the remaining, but no longer refreshed, electron-positron pairs had annihilated and contributed to the total photon energy. The related temperatures
T
g
{\displaystyle \;T_{\mathrm {\gamma } }\;}
and
T
n
{\displaystyle \;T_{\mathrm {\nu } }\;}
are the simultaneous temperatures of the photons (g) and neutrinos (n) respectively, whose ratio stays "stuck" at the same value indefinitely, after
T
g
< T 1 . {\displaystyle \;T_{\mathrm {\gamma } }