In Big Bang cosmology, neutrino decoupling refers to the epoch at which neutrinos ceased interacting with baryonic matter, and thereby ceased influencing the dynamics of the universe at early times. Prior to decoupling, neutrinos were in thermal equilibrium with protons, neutrons, and electrons, which was maintained through the weak interaction. Decoupling occurred approximately at the time when the rate of those weak interactions was slower than the rate of expansion of the universe. Alternatively, it was the time when the time scale for weak interactions became greater than the age of the universe at that time. Neutrino decoupling took place approximately one second after the Big Bang, when the temperature of the universe was approximately 10 billion kelvins, or 1 MeV.
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Derivation of decoupling time
Neutrinos are scattered (interfering with free streaming) by their interactions with electrons and positrons, such as the reaction
The approximate rate of these interactions is set by the number density of electrons and positrons, the averaged product of the cross section for interaction and the velocity of the particles. The number density
This can be compared to the expansion rate which is given by the Hubble parameter
where
Solving for temperature gives
While this is a very rough derivation, it illustrates the important physical phenomena which determined when neutrinos decoupled.
Observational evidence
While neutrino decoupling can not be observed directly, it is expected to have left behind a cosmic neutrino background, analogous to the cosmic microwave background radiation of visible light which was emitted at a much later epoch. "The detection of the neutrino background is far beyond the capabilities of the present generation of neutrino detectors." There is data, however, which indirectly indicates the presence of a neutrino background. One piece of evidence is damping of the angular power spectrum of the CMB, which results from anisotropies in the neutrino background.
Another indirect measurement of neutrino decoupling is allowed by the role that neutrino decoupling plays in setting the ratio of neutrons to protons. 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