Neutrino decoupling

After 1 s or so, the neutrinos decouple from the cosmic plasma and expand isentropically for ever afterwards remaining as microwave neutrinos with... 

At temperatures above a few MeV, when the universe is tens of milliseconds old, interactions among photons, neutrinos, electrons, and positrons establish and maintain equilibrium (T7 = TV = Te). When the temperature drops below a few MeV the weakly interacting neutrinos decouple, continuing to cool and dilute along with the expansion of the universe (T oc a-1, nv oc 7j), and pv oc 7))). 

As the weak interaction is the slowest of all, it was the first to find itself unable to keep up with the rapid expansion of the Universe. The neutrinos it produces, which serve as an indicator of the weak interaction, were the first to experience decoupling, the particle equivalent of social exclusion. By the first second, expansion-cooled neutrinos ceased to interact with other matter in the form of protons and neutrons. This left the latter free to organise themselves into nuclei. Indeed, fertile reactions soon got under way between protons and neutrons. However, the instability of species with atomic masses between 5 and 8 quickly put paid to this first attempt at nuclear architecture. The two species of nucleon, protons and neutrons, were distributed over a narrow range of nuclei from hydrogen to lithium-7, but in a quite unequal way. 

As it is seen, the equations are decoupled if p = 0. As a consequence we obtain the two-component model of mass-less neutrino with corresponding to the right and - to the left neutrino [8]. 

A neutrino lighter than 1 MeV decouples while relativistic. If it is so light to be still relativistic today (rnv 0.1 meV), its relic density is pp = 77t27 / I20. If it became non-relativistic after decoupling, its relic density is determined by its equilibrium number density as pv = mI,3C(3)T,3/27r2. Here Tv = (3/ll)1//3T7, where T7 = 2.725 0.002K is the cosmic microwave background temperature. (We use natural units, c- h, I.)... 

As the universe expands and cools below the electron rest mass energy, the e pairs annihilate, heating the CMB photons, but not the neutrinos which have already decoupled. The decoupled neutrinos continue to cool by the expansion of the universe (T oc a-1), as do the photons which now have a higher temperature T1 = (11 /4)4/3T (n7/n = 11/3). During these epochs... 

First, the weak interaction quanta became massive at the temperature scale of 100 GeV. Since then, weak reactions have only occurred in contact interactions of the particles. At about the same time the t-quark and the Higgs quanta also decoupled from the soup. The same decoupling happened for the other heavy quark species (b-quark, c-quark) and for the heaviest of the leptons (r-particle) in the range 1-5 GeV (a few times lO K) of the average energy density. The x-neutrinos remain in thermal equilibrium via weak neutral interactions. 

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