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	~~I would like~~ to ~~introduce myself~~ to ~~you~~, ~~I am Andrew~~ and ~~my spouse doesn't like it at all~~. ~~Ohio~~ is where ~~her home~~ is. ~~As a lady what she truly likes~~ is ~~style~~ and ~~she~~'~~s been doing~~ it for ~~fairly~~ a ~~whilst~~. ~~Credit authorising~~ is ~~how she makes~~ a ~~residing~~.<br><br>~~Also visit my site: psychic solutions~~ by ~~lynne~~ ([~~http~~:/~~/modenpeople~~.co.kr/~~modn~~/~~qna~~/~~292291 http:~~//~~modenpeople~~.co.kr/~~modn~~/~~qna~~/~~292291~~])		{{Cosmology\|cTopic=Early universe}}

			The '''cosmic neutrino background''' (CNB, CνB{{ref\|nu}}) is the universe's background particle radiation composed of [[neutrino]]s. They are sometimes known as '''relic neutrinos'''.

			Like the [[cosmic microwave background radiation]] (CMB), the CνB is a relic of the [[big bang]], and while the CMB dates from when the universe was 379,000 years old, the [[Neutrino decoupling\|CνB decoupled]] from matter when the universe was 2 seconds old. It is estimated that today the CνB has a temperature of roughly {{val\|1.95\|ul=K}}. Since low-energy neutrinos interact only very weakly with matter, they are notoriously difficult to detect and the CνB might never be observed directly. There is, however, compelling [[Cosmic neutrino background#Indirect evidence for the CνB\|indirect evidence]] for its existence.

			==Derivation of the temperature of the CνB==
			Given the temperature of the CMB, the temperature of the CνB can be estimated. Before [[neutrino decoupling\|neutrinos decoupled]] from the rest of matter, the universe primarily consisted of neutrinos, [[electron]]s, [[positron]]s, and [[photon]]s, all in [[thermal equilibrium]] with each other. Once the temperature reached approximately {{val\|2.5\|ul=MeV}}, 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 '''''σ''''' is the entropy, '''''g''''' is the effective [[Degrees of freedom (statistics)\|degrees of freedom]] and '''''T''''' is the temperature, we find that

			:<math>\left(\frac{g_0}{g_1}\right)^{1/3} = \frac{T_1}{T_0}</math>,

			where '''''T<sub>0</sub>''''' denotes the temperature before the electron-positron annihilation and '''''T<sub>1</sub>''''' denotes after. The factor '''''g<sub>0</sub>''''' is determined by the particle species:

			*2 for photons, since they are massless [[bosons]]<ref name=Weinberg_Cosmology>{{cite book \|url=http://books.google.com/books?id=48C-ym2EmZkC&pg=PA3 \|author=Steven Weinberg \|title=Cosmology \|publisher=Oxford University Press \|page=151 \|year=2008 \|isbn=978-0-19-852682-7}}</ref>
			*2(7/8) each for electrons and positrons, since they are [[fermions]].<ref name=Weinberg_Cosmology />

			'''''g<sub>1</sub>''''' 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 '''''T<sub>γ</sub>''''' = {{val\|2.725\|u=K}},<ref>{{cite journal\|first=Dale\|last=Fixsen\|coauthors=Mather, John\|title=The Spectral Results of the Far-Infrared Absolute Spectrophotometer Instrument on COBE\|year=2002\|journal=Astrophysical Journal\|volume=581\|issue=2\|pages=817–822\|bibcode=2002ApJ...581..817F\|doi=10.1086/344402}}</ref> it follows that '''''T<sub>ν</sub>''''' ≈ {{val\|1.95\|u=K}}.

			The above discussion is valid for massless neutrinos, which are always relativistic. For neutrinos with a non-zero rest mass, the description in terms of a temperature is no longer appropriate after they become non-relativistic; i.e., when their thermal energy 3/2 '''''kT<sub>ν</sub>''''' falls below the rest mass energy '''''m<sub>ν</sub>c<sup>2</sup>'''''. Instead, in this case one should rather track their energy density, which remains well-defined.

			== Indirect evidence for the CνB ==
			Relativistic neutrinos contribute to the radiation energy density of the Universe '''''ρ<sub>R</sub>''''', typically parameterized in terms of the effective number of neutrino species '''''N<sub>ν</sub>''''':
			:<math> \rho_{\rm R} = \frac{\pi^2}{15} \, T_\gamma^4 (1+z)^4 \left[ 1 + \frac{7}{8} N_{\rm \nu} \left( \frac{4}{11} \right)^{4/3} \right],</math>
			where '''''z''''' denotes the [[redshift]]. The first term in the square brackets is due to the CMB, the second comes from the CνB. The [[Standard Model]] with its three neutrino species predicts a value of
			'''''N<sub>ν</sub>''''' ≃ {{val\|3.046}},<ref>{{cite journal \| first = Gianpiero \| last = Mangano \| coauthors = et al. \| title = Relic neutrino decoupling including flavor oscillations \| year = 2005 \| journal = Nucl.Phys.B \| volume = 729 \| issue = 1–2 \| pages = 221–234 \| arxiv = hep-ph/0506164 \| doi = 10.1016/j.nuclphysb.2005.09.041\|bibcode = 2005NuPhB.729..221M }}</ref> including a small correction caused by a non-thermal distortion of the spectra during [[Positron\|e<sup>+</sup>]]-[[Electron\|e<sup>-</sup>]]-[[annihilation]]. The radiation density had a major impact on various physical processes in the early Universe, leaving potentially detectable imprints on measurable quantities, thus allowing us to [[inference\|infer]] the value of '''''N<sub>ν</sub>''''' from observations.

			=== Big Bang Nucleosynthesis ===
			Due to its effect on the [[Metric expansion of space\|expansion rate]] of the Universe during [[Big Bang nucleosynthesis]] (BBN), the theoretical expectations for the primordial abundances of light elements depend on '''''N<sub>ν</sub>'''''. Astrophysical measurements of the primordial {{SimpleNuclide2\|Helium\|link=yes}} and {{SimpleNuclide2\|Deuterium\|link=yes}} abundances lead to a value of '''''N<sub>ν</sub>''''' = {{val\|3.14\|+0.70\|-0.65}} at 68% [[confidence interval\|c.l.]],<ref>{{cite journal \| first = Richard \| last = Cyburt \| coauthors = et al. \| title = New BBN limits on physics beyond the standard model from He-4 \| year = 2005 \| journal = Astropart.Phys. \| volume = 23 \| issue = 3 \| pages = 313–323 \| arxiv = astro-ph/0408033 \| doi = 10.1016/j.astropartphys.2005.01.005\|bibcode = 2005APh....23..313C }}</ref> in very good agreement with the Standard Model expectation.

			=== CMB anisotropies and structure formation ===
			The presence of the CνB affects the evolution of CMB anisotropies as well as the growth of matter perturbations in two ways: due to its contribution to the radiation density of the Universe (which determines for instance the time of matter-radiation equality), and due to the neutrinos' anisotropic stress which dampens the acoustic oscillations of the spectra. Additionally, [[free-streaming]] massive neutrinos suppress the growth of structure on small scales. The [[Wilkinson Microwave Anisotropy Probe\|WMAP]] spacecraft's five-year data combined with type Ia [[supernova]] data and information about the [[baryon acoustic oscillation]] scale yield '''''N<sub>ν</sub>''''' = {{val\|4.34\|+0.88\|-0.86}} at 68% c.l.,<ref>{{cite journal \| first = Eiichiro \| last = Komatsu \| coauthors = et al. \| title = Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation \| year = 2010 \| arxiv = 1001.4538\|bibcode = 2011ApJS..192...18K \|doi = 10.1088/0067-0049/192/2/18 \| journal = The Astrophysical Journal Supplement Series \| volume = 192 \| issue = 2 \| pages = 18 }}</ref> providing an independent confirmation of the BBN constraints. In the near future, probes such as the [[Planck (spacecraft)\|Planck spacecraft]] will likely improve present errors on '''''N<sub>ν</sub>''''' by an order of magnitude.<ref>{{cite journal \| first = Sergej \| last = Bashinsky \| coauthors = Seljak, Uroš \| title = Neutrino perturbations in CMB anisotropy and matter clustering \| year = 2004 \| journal = Phys. Rev. D \| volume = 69 \| issue = 8 \| pages = 083002 \| arxiv = astro-ph/0310198 \| doi = 10.1103/PhysRevD.69.083002\|bibcode = 2004PhRvD..69h3002B }}</ref>

			==See Also==
			[[Dark matter]]

			==Notes==
			#{{note\|nu}}ν (italic ''ν'') is the Greek letter ''[[nu (letter)\|nu]]'', standardized symbol for ''neutrinos''.

			==References==
			{{reflist\|1}}

			[[Category:Physical cosmology]]
			[[Category:Cosmic background radiation]]

en>Wbm1058: Undid revision 457131208 by 84.50.105.50 (talk) article not about sports, Conversion rate is a different concept per linked article

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Undid revision 457131208 by 84.50.105.50 (talk) article not about sports, Conversion rate is a different concept per linked article

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I would like to introduce myself to you, I am Andrew and my spouse doesn't like it at all. Ohio is where her home is. As a lady what she truly likes is style and she's been doing it for fairly a whilst. Credit authorising is how she makes a residing.<br><br>Also visit my site: psychic solutions by lynne ([http://modenpeople.co.kr/modn/qna/292291 http://modenpeople.co.kr/modn/qna/292291])

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en>EmausBot: Bot: Migrating 1 interwiki links, now provided by Wikidata on d:Q13217979

en>Wbm1058: Undid revision 457131208 by 84.50.105.50 (talk) article not about sports, Conversion rate is a different concept per linked article