The cosmic neutrino background (CNB or CB) is the universe's background particle radiation composed of neutrinos. They are sometimes known as relic neutrinos.
The CB 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 CB decoupled (separated) from matter when the universe was just one second old. It is estimated that today, the CB has a temperature of roughly .
As neutrinos rarely interact with matter, these neutrinos still exist today. They have a very low energy, around 10 to 10 eV. Even high energy neutrinos are notoriously difficult to detect, and the CB has energies around 1010 times smaller, so the CB may not be directly observed in detail for many years, if at all. However, Big Bang cosmology makes many predictions about the CB, and there is very strong indirect evidence that the CB exists.
Derivation of the CB temperature
Given the temperature of the cosmic microwave background (CMB) the temperature of the cosmic neutrino background (CB) can be estimated. It involves a change between two regimes: Regime 1 The original state of the universe is a thermal equilibrium, the final stage of which has photons and leptons freely creating each other through annihilation (leptons create photons) and pair production (photons create leptons). This was the very brief state, right after the Big Bang. Its last stage involves only the lowest-mass possible fermions that interact with photons: electrons and positrons.
Regime 2 Once the universe has expanded enough that the photon+lepton plasma has cooled to the point that Big Bang photons no longer have enough energy for pair production of the lowest mass/energy leptons, the remaining electron–positron pairs annihilate. The photons they create are cool, and are then unable to create new particle pairs. This is the current state of most of the universe.
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 ( K), the neutrinos decoupled from the rest of matter, and for practical purposes, all lepton and photon interactions with these neutrinos stopped.
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 of the universe was approximately conserved by the electron–positron annihilation. Then using
where is the effective number of degrees of freedom and is the plasma or photon temperature. Once reactions cease, the entropy should remain approximately "stuck" for all temperatures below the cut-off temperature, and we find that
Here denotes the lowest temperature where pair production and annihilation were in equilibrium; and denotes the temperature after the temperature fell below the regime-shift temperature , after the remaining, but no longer refreshed, electron–positron pairs had annihilated and contributed to the total photon energy. The related temperatures and are the simultaneous temperatures of the photons () and neutrinos () respectively, whose ratio stays "stuck" at the same value indefinitely, after
The factor is determined by a sum, based on the particle species engaged in the original equilibrium reaction: + 2 for each photon (or other massless bosons, if any). + for each electron, positron, or other fermion. Whereas the factor is simply 2, since the present regime only concerns photons, in thermal equilibrium with at most themselves.
So
Since the cosmic photon background temperature at present has cooled to it follows that the neutrino background temperature is currently