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It is reasonable to assume that for each species, the concentration of neu- trinos equals the concentration of antineutrinos, so that their chemical potentials are equal: uv = µũ. Furthermore, neutrinos and antineutrinos can be produced and annihilated in pairs by the reaction v +ū+ 2y (where y is a photon). Assuming that this reaction is at equilibrium (as it would have been in the very early universe), prove that u = 0 for both the neutrinos and the antineutrinos.

It is reasonable to assume that for each species, the concentration of neu- trinos equals the concentration of antineutrinos, so that their chemical potentials are equal: uv = µũ. Furthermore, neutrinos and antineutrinos can be produced and annihilated in pairs by the reaction v +ū+ 2y (where y is a photon). Assuming that this reaction is at equilibrium (as it would have been in the very early universe), prove that u = 0 for both the neutrinos and the antineutrinos.

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In addition to the cosmic background radiation of photons, the universe is thought to be permeated with a background radiation of neutrinos (v) and antineutrinos (v ), currently at an effective temperature of 1.95 K. There are three species of neutrinos, each of which has an antiparticle, with only one allowed polarization state for each particle or antiparticle. For parts (a) through (c) below, assume that all three species are exactly massless.

It is reasonable to assume that for each species, the concentration of neu- trinos equals the concentration of antineutrinos, so that their chemical potentials are equal: uv = µũ. Furthermore, neutrinos and antineutrinos can be produced and annihilated in pairs by the reaction v +ū+ 2y (where y is a photon). Assuming that this reaction is at equilibrium (as it would have been in the very early universe), prove that u = 0 for both the neutrinos and the antineutrinos.
Transcribed Image Text:It is reasonable to assume that for each species, the concentration of neu- trinos equals the concentration of antineutrinos, so that their chemical potentials are equal: uv = µũ. Furthermore, neutrinos and antineutrinos can be produced and annihilated in pairs by the reaction v +ū+ 2y (where y is a photon). Assuming that this reaction is at equilibrium (as it would have been in the very early universe), prove that u = 0 for both the neutrinos and the antineutrinos.
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