Cosmic neutrino background
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2008-03-08T23:21:41Z
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clarifications, and noticed that NASA doesn't capitalize "cosmic neutrino background"
{{Cosmology|cTopic=Early universe}}
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The '''cosmic neutrino background''' (CNB) is the universe's background particle radiation composed of [[neutrino]]s.
Like the [[cosmic microwave background radiation]] (CMB), the CNB is a relic of the [[big bang]], and while the CMB dates from when the universe was 380,000 years old, the CNB decoupled from matter when the universe was 2 seconds old. It is estimated that the CNB has a temperature of 1.9 kelvins or lower. Neutrinos are notoriously difficult to detect, and because the cosmic neutrinos are so cold, the CNB might never be observed directly.
== Derivation of the temperature of the CNB ==
Given the temperature of the CMB, the temperature of the CNB can be estimated. 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 below the masses of the [[W and Z bosons]], the neutrinos decoupled from the rest of matter. Despite this decoupling, neutrinos and photons remained at the same temperature as the universe expanded. However, when the temperature dropped below the mass of the electron, most [[electron-positron annihilation|electrons and positrons annihilated]], transferring their heat and entropy to photons, and 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 photons and the neutrinos today. To find this ratio, we assume that the entropy of the universe was approximately conserved by the electron-positron annihilation. Then using
:<math>\sigma \propto gT^3</math>,
where <math>\sigma</math> is the entropy, <math>g</math> is the effective number of [[degrees of freedom]] and <math>T</math> is the temperature, we find that
:<math>\left(\frac{g_0}{g_1}\right)^{1/3} = \frac{T_1}{T_0}</math>,
where the subscript 0 denotes before the electron-positron annihilation and 1 denotes after. To find <math>g_0</math>, we add the degrees of freedom for electrons, positrons and photons:
* 2 for photons, since they are massless [[bosons]]
* 2(7/8) each for electrons and positrons, since they are [[fermions]]
<math>g_1</math> is just 2 for photons. So
:<math>\frac{T_\nu}{T_\gamma} = \left(\frac{4}{11}\right)^{1/3}</math>.
Given the current value of <math>T_\gamma = 2.73 \rm K</math>, it follows that <math>T_\nu \approx 1.9 \rm K</math>.
The above discussion is valid for massless neutrinos, which are always relativistic.
If neutrinos have a positive rest mass, they become non-relativistic when the thermal
energy <math> 3/2 kT_\nu </math> falls well below the rest mass energy <math> m_\nu c^2 </math>.
Non-relativistic matter cools faster than relativistic matter as the Universe expands.
Precise calculations, keeping the entropy of each fermion constant,
give for today's neutrino temperature
<math>T_\nu \approx 1.6 \cdot 10^{-4} \left(m_\nu / 1 \rm eV \right)^{-1} \rm K</math>.
==See also==
* [[Cosmic microwave background]]
{{astronomy-stub}}
[[Category:Physical cosmology]]
[[es:Fondo cósmico de neutrinos]]
[[fi:Kosminen neutriinotausta]]
[[fr:Fond cosmologique de neutrinos]]