[2] Prior to decoupling, neutrinos were in thermal equilibrium with protons, neutrons and electrons, which was maintained through the weak interaction.
The neutrinos from this event have a very low energy, around 10−10 times smaller than is possible with present-day direct detection.
[4] Even high energy neutrinos are notoriously difficult to detect, so the CNB may not be directly observed in detail for many years, if at all.
The product of the cross section and velocity for weak interactions for temperatures (energies) below W/Z boson masses (~100 GeV) is given approximately by
is Fermi's constant (as is standard in particle physics calculations, factors of the speed of light
As the rate of weak interaction depends more strongly on temperature, it will fall more quickly as the universe cools.
Thus when the two rates are approximately equal (dropping terms of order unity, including an effective degeneracy term which counts the number of states of particles which are interacting) gives the approximate temperature at which neutrinos decouple: Solving for temperature gives While this is a very rough derivation, it illustrates the important physical phenomena which determined when neutrinos decoupled.
One piece of evidence is damping of the angular power spectrum of the CMB, which results from anisotropies in the neutrino background.
Before decoupling, the number of neutrons and protons are maintained in their equilibrium abundances by weak interactions, specifically beta decay and electron capture (or inverse beta decay) according to and Once the rate of weak interactions is slower than the characteristic rate of the expansion of the universe, this equilibrium cannot be maintained, and the abundance of neutrons to protons "freezes in," at a value This value is simply found by evaluating the Boltzmann factor for neutrons and protons at decoupling time, according to where
Thus the abundance of neutrons in the primordial matter can be measured by astronomers, and, as it was determined by the ratio of neutrons to protons at neutrino decoupling, the helium abundance indirectly measures the temperature at which neutrino decoupling took place, and is in agreement with the figure derived above.
[10] Big Bang cosmology makes many predictions about the CNB, and there is very strong indirect evidence that the cosmic neutrino background exists, both from Big Bang nucleosynthesis predictions of the helium abundance, and from anisotropies in the cosmic microwave background.
One of these predictions is that neutrinos will have left a subtle imprint on the cosmic microwave background (CMB).
Some of the CMB fluctuations were roughly regularly spaced, because of the effect of baryon acoustic oscillations.
In theory, the decoupled neutrinos should have had a very slight effect on the phase of the various CMB fluctuations.