View source for Cosmic neutrino background

{{Short description|Universe's background particle radiation composed of neutrinos}}
{{Cosmology|early}}
{{use dmy dates|date=July 2021}}
The '''cosmic neutrino background''' ('''CNB''' or '''C{{math|ν}}B'''{{efn|The symbol {{math|ν}} (italic {{mvar|ν}}) is the Greek letter ''[[nu (letter)|nu]]'', standard [[particle physics]] symbol for a ''[[neutrino]]''. In this article, it is set in a mathematical font in order to help distinguish its shape from the extremely similar lower-case Latin letter&nbsp;"v", which in a sans-serif font is identical: Greek "ν" vs. Latin "v".}}) is the universe's background particle radiation composed of [[neutrino]]s. They are sometimes known as '''relic neutrinos'''.

The C{{math|ν}}B is a relic of the [[Big Bang]]; while the [[cosmic microwave background radiation]] (CMB) dates from when the universe was 379,000&nbsp;years old, the [[Neutrino decoupling|C{{math|ν}}B decoupled]] (separated) from matter when the universe was just one&nbsp;second old. It is estimated that today, the C{{math|ν}}B has a temperature of roughly {{val|1.95|ul=K}}.

As neutrinos rarely interact with matter, these neutrinos still exist today. They have a very low energy, around 10{{sup|−4}} to 10{{sup|−6}} [[electron volt|eV]].<ref name=Follin-Knox-Millea-Pan-2015/>{{refn|name=Forbes-2016-09-09-cosmic-ν}} Even high energy neutrinos are [[neutrino detector|notoriously difficult to detect]], and the C{{math|ν}}B has energies around 10<sup>10</sup>&nbsp;times smaller, so the C{{math|ν}}B may not be directly observed in detail for many years, if at all.<ref name=Follin-Knox-Millea-Pan-2015/>{{refn|name=Forbes-2016-09-09-cosmic-ν}} However, [[Big Bang]] cosmology makes many predictions about the C{{math|ν}}B, and there is very strong indirect evidence that the C{{math|ν}}B exists.<ref name=Follin-Knox-Millea-Pan-2015/>{{refn|name=Forbes-2016-09-09-cosmic-ν|
{{cite news
 |title=Cosmic neutrinos detected, confirming the Big Bang's last great prediction
 |date=2016-09-09
 |series=Starts with a Bang 
 |magazine=[[Forbes]]
 |url=https://www.forbes.com/sites/startswithabang/2016/09/09/cosmic-neutrinos-detected-confirming-the-big-bangs-last-great-prediction
}}
<br/>
Above is news coverage of the original academic paper:<ref name=Follin-Knox-Millea-Pan-2015/>
}}

==Temperature estimation==
Given the temperature of the [[cosmic microwave background]] (CMB) the temperature of the cosmic neutrino background (C{{math|ν}}B) can be estimated. It involves a change between two regimes:
;Regime 1: The original state of the universe is a thermal equilibrium, the final stage of which has [[photon]]s and [[lepton]]s freely creating each other through [[annihilation]] (leptons create photons) and [[pair production]] (photons create leptons). This was the very brief state, right after the Big Bang. Its last stage involves only the lowest-mass possible [[fermion]]s that interact with photons: [[electron]]s and [[positron]]s.

;Regime 2: Once the universe has expanded enough that the photon+lepton plasma has cooled to the point that [[cosmic microwave background|Big Bang photons]] no longer have enough energy for [[pair production]] of the lowest mass/energy leptons, the remaining [[electron]]–[[positron]] pairs annihilate. The photons they create are cool, and are then unable to create new particle pairs. This is the current state of most of the universe.{{efn|The exceptions are nuclear processes inside [[star]]s and [[white dwarfs]]. These produce "hot" neutrinos, unlike the "cold" C{{math|ν}}B. ''See'' [[Neutrino]] § [[Neutrino#Solar|Solar]].}}

At very high temperatures, 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 dropped to approximately {{val|2.5|ul=MeV}} (<math>17.4\times 10^9</math>  K), the neutrinos decoupled from the rest of matter, and for practical purposes, all lepton and photon interactions with these neutrinos stopped.{{efn|
The neutrino interactions that are measured in current particle detectors are all with neutrinos newly [[neutrino#Solar|created in the Sun]], [[neutrino#Reactor neutrinos|nuclear reactors]], [[neutrino#Nuclear weapons|weapons]], [[neutrino#Accelerator neutrinos|particle accelerators]], [[neutrino#Atmospheric|cosmic ray collisions]], and [[SuperNova Early Warning System|supernova]]s. Even among those, only the neutrinos with the highest kinetic energies are feasibly detectable. It is something of a "lose-lose" situation: The lower a neutrino's kinetic energy, the lower its probability of interacting with matter, and the even slighter, less noticeable, the matter's response will be even if some rare event were to occur.
}}

Despite this decoupling, neutrinos and photons remained at the same temperature as the universe expanded as a "fossil" of the prior Regime&nbsp;1, since both are cooled in the same way by the same process of [[cosmic expansion]], from the same starting temperature. However, when the temperature dropped below double the mass of the electron, most [[electron–positron annihilation|electrons and positrons annihilated]], transferring their heat and entropy to photons, 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 neutrinos and the photons in the current Regime&nbsp;2. To find this ratio, we assume that the entropy &nbsp;{{mvar|s}}&nbsp; of the universe was approximately conserved by the electron–positron annihilation. Then using

:<math> s \propto g \, T^3 ~,</math>

where &nbsp;{{mvar|g}}&nbsp; is the [[degrees of freedom (physics and chemistry)|''effective number of degrees of freedom'']] and {{mvar|T}} is the plasma or photon temperature. Once reactions cease, the entropy &nbsp;{{mvar|s}}&nbsp; should remain approximately "stuck" for all temperatures below the cut-off temperature, and we find that

:<math>\frac{\; T_1 \;}{T_2} = \left(\frac{\; g_2 \;}{g_1}\right)^{\tfrac{1}{3}}~,</math>

Here <math>\; T_1 \propto T_\mathrm{\nu} \;</math> denotes the lowest temperature where [[pair production]] and [[annihilation]] were in equilibrium; and <math>\; T_2 \propto T_\mathrm{\gamma} \;</math> denotes the temperature after the temperature fell below the regime-shift temperature <math>\; T_1 \;</math>, after the remaining, but no longer refreshed, [[electron]]–[[positron]] pairs had [[annihilated]] and contributed to the total photon energy. The related temperatures <math>\; T_\mathrm{\gamma} \;</math> and <math>\; T_\mathrm{\nu} \;</math> are the simultaneous temperatures of the photons ({{math|γ}}) and neutrinos  ({{math|&nu;}}) respectively, whose ratio stays "stuck" at the same value indefinitely, after <math>\; T_\mathrm{\gamma} < T_1 \;.</math>

The factor <math>\; g_1 \;</math> is determined by a sum, based on the particle species engaged in the original equilibrium reaction:
: + &nbsp; 2 &nbsp; for each photon (or other massless [[bosons]], if any).<ref name=Weinberg-2008-Cosmology/>
: + &nbsp; {{sfrac|7|4}} &nbsp; for each electron, positron, or other [[fermion]].<ref name=Weinberg-2008-Cosmology/>
Whereas the factor <math>\; g_2 \;</math> is simply &nbsp; 2, &nbsp; since the present regime only concerns photons, in thermal equilibrium with at most themselves.<ref name=Weinberg-2008-Cosmology>
{{cite book
 |author-link=Steven Weinberg |last=Weinberg |first=S.
 |year=2008
 |title=Cosmology
 |page=151
 |publisher=[[Oxford University Press]]
 |isbn=978-0-19-852682-7
 |url=https://books.google.com/books?id=48C-ym2EmZkC&pg=PA3
}}
</ref>

So
:<math>\frac{\; T_\mathrm{\nu} \;}{T_\mathrm{\gamma} } = \frac{\; T_1 \;}{T_2} = \left(\frac{\; g_2 \;}{g_1}\right)^{\tfrac{1}{3}} = \left( \frac{ 2 }{\; 2 + \tfrac{7}{4} + \tfrac{\,7\,}{4} \;} \right)^{\tfrac{\,1\,}{3}} = \left( \frac{4}{\; 11 \;} \right)^{\tfrac{\,1\,}{3}} \approx {0.714} ~.</math>

Since the cosmic photon background temperature at present has cooled to <math>\; T_\mathrm\gamma = 2.725\,\mathrm{ K } ~ ,</math><ref name=Fixsen-Mather-2002>
{{cite journal
 |first1=Dale  |last1=Fixsen
 |first2=John  |last2=Mather
 |year=2002
 |title=The spectral results of the Far-Infrared Absolute Spectrophotometer instrument on COBE
 |journal=[[Astrophysical Journal]]
 |volume=581  |issue=2  |pages=817–822
 |bibcode=2002ApJ...581..817F
 |doi=10.1086/344402  |doi-access=free
}}
</ref> it follows that the neutrino background temperature is currently
: <math>\; T_\mathrm\nu \approx {1.95}\,\mathrm{ K }~.</math>

The above discussion is technically valid for massless neutrinos, which are always relativistic. For neutrinos with a non-zero rest mass, at low temperature where the neutrinos become non-relativistic, a description in terms of a temperature is not appropriate. In other words, when the neutrinos' thermal energy <math>\; \frac{3}{2}\, k\,T_\mathrm{\nu} \;</math> ({{mvar|k}} is the [[Boltzmann constant]]) falls below the rest mass energy <math>\; m_\mathrm{\nu} \,c^2 \; ;</math> in a low-temperature case one should instead speak of the neutrinos' collective energy ''density'', which remains both relevant and well-defined.

== Indirect evidence ==
Relativistic neutrinos contribute to the radiation energy density of the universe {{mvar|ρ}}{{sub|R}}, typically parameterized in terms of the effective number of neutrino species {{mvar|N}}{{math|{{sub|ν}} }}:

:<math>\rho_\mathrm{R} = \frac{\pi^2}{15} T_\mathrm{\gamma}^4 (1 + z)^4 \left[ 1 + \frac{7}{8} N_\mathrm{\nu} \left( \frac{4}{11} \right)^{\frac{4}{3}} \right],</math>

where {{mvar|z}} denotes the [[redshift]]. The first term in the square brackets is due to the CMB, the second comes from the C{{math|ν}}B. The [[Standard Model]] with its three neutrino species predicts a value of {{mvar|N}}{{math|{{sub|ν}} ≃ }}{{val|3.046}},<ref name=Gianpiero-etal-2005/> including a small correction caused by a non-thermal distortion of the spectra during [[Positron|e{{sup|+}}]]×[[Electron|e{{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  {{mvar|N}}{{math|{{sub|ν}} }} 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 {{mvar|N}}{{math|{{sub|ν}}.}} Astrophysical measurements of the primordial {{SimpleNuclide |Helium| link=yes}} and {{SimpleNuclide|Deuterium|link=yes}} abundances lead to a value of {{mvar|N}}{{math|{{sub|ν}} }} = {{val|3.14|+0.70|−0.65}} at 68% [[confidence interval|c.l.]],<ref name=Cyburt-etal-2005/> in very good agreement with the Standard Model expectation.

=== From the cosmic microwave background ===

==== Anisotropies and structure formation ====
The presence of the C{{math|ν}}B 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 yielded {{mvar|N}}{{math|{{sub|ν}} }} = {{val|4.34|+0.88|−0.86}} at 68% [[confidence limit|c.l.]],<ref name=Komatsu-WMAP-etal-2011/> providing an independent confirmation of the BBN constraints. The [[Planck (spacecraft)|Planck spacecraft]] collaboration has published the tightest bound to date on the effective number of neutrino species, at {{mvar|N}}{{math|{{sub|ν}} }} = {{val|3.15|0.23}}.<ref name=Ade-Planck-etal-2016/>

==== Phase changes ====
Big Bang cosmology makes many predictions about the C{{math|ν}}B, and there is very strong indirect evidence that the cosmic neutrino background exists, both from [[Big Bang nucleosynthesis]] predictions of the helium abundance, and from anisotropies in the [[cosmic microwave background]]. One of these predictions is that neutrinos will have left a subtle imprint on the cosmic microwave background (CMB). It is well known that the CMB has irregularities. Some of the CMB fluctuations were roughly regularly spaced, because of the effect of [[baryon acoustic oscillation]]. In theory, the decoupled neutrinos should have had a very slight effect on the [[Phase (waves)|phase]] of the various CMB fluctuations.<ref name=Follin-Knox-Millea-Pan-2015/>{{refn|name=Forbes-2016-09-09-cosmic-ν}}

In 2015, it was reported that such shifts had been detected in the CMB. Moreover, the fluctuations corresponded to neutrinos of almost exactly the temperature predicted by [[Big Bang theory]] ({{nowrap|1.96 ± 0.02&nbsp;K}} compared to a prediction of 1.95&nbsp;K), and exactly three types of neutrino, the same number of neutrino flavours currently predicted by the [[Standard Model]].<ref name=Follin-Knox-Millea-Pan-2015/>{{refn|name=Forbes-2016-09-09-cosmic-ν}}

==Prospects for the direct detection==
Confirmation of the existence of these relic neutrinos may only be possible by directly detecting them using experiments on Earth. This will be difficult as the neutrinos which make up the C{{math|ν}}B are non-relativistic, in addition to interacting only weakly with normal matter, and so any effect they have in a detector will be hard to identify. One proposed method of direct detection of the C{{math|ν}}B is to use the capture of cosmic relic neutrinos on [[tritium]] i.e. <sup>3</sup>H, leading to an induced form of [[beta decay]].<ref name=Long-Lunardn-Sabanclr-2014/>

The neutrinos of the C{{math|ν}}B would lead to the production of electrons via the reaction
: <math> \mathrm{\nu} + {}^3\mathrm{H} \rightarrow {}^3\mathrm{He} + e^{-} ~,</math>

while the main background comes from electrons produced via natural beta decay
: <math> {}^3\mathrm{H} \rightarrow {}^3\mathrm{He} + e^{-} + \mathrm{\bar{\nu}} ~.</math>

These electrons would be detected by the experimental apparatus in order to measure the size of the C{{math|ν}}B. The latter source of electrons is far more numerous, however, their maximum energy is smaller than the average energy of the C{{math|ν}}B-electrons by twice the average neutrino mass. Since this mass is tiny, of the order of a few [[Electronvolt|eV]]s or less, such a detector must have an excellent energy resolution in order to separate the signal from the background. One such proposed experiment is called PTOLEMY, which will be made up of 100 g of tritium target.<ref name=Betts-PTOLEMY-etal-2013/> The detector demonstrator (with about 0.2 g of tritium) should be ready by 2025.<ref name=Mangano-PTOLEMY-etal-2019/>

==See also==

*[[Cosmic background radiation]]
*[[Dark matter]]
*[[Diffuse supernova neutrino background]]
*[[Gravitational wave background]]

==Notes==
{{notelist}}

==References==
{{reflist|refs=

<ref name=Ade-Planck-etal-2016>
{{cite journal
 | first1 = P.A.R. | last1 = Ade
 | display-authors=etal
 | year = 2016
 | title = Planck&nbsp;2015 results. XIII. Cosmological parameters
 | journal = Astronomy & Astrophysics
 | volume = 594 | issue = | page = A13
 | bibcode = 2016A&A...594A..13P  | s2cid = 119262962
 | arxiv=1502.01589  |doi = 10.1051/0004-6361/201525830
}}
</ref>

<ref name=Betts-PTOLEMY-etal-2013>
{{cite arXiv
 |last1= Betts  |first1=S.
 |display-authors=etal
 |collaboration=PTOLEMY collaboration
 |year= 2013
 |title= Development of a relic neutrino detection experiment at PTOLEMY: Princeton Tritium Observatory for Light, Early-Universe, Massive-Neutrino Yield
 |class= astro-ph.IM
 |eprint=1307.4738
}}
</ref>

<ref name=Cyburt-etal-2005>
{{cite journal
 | first1 = Richard | last1 = Cyburt
 | display-authors=etal
 | year = 2005
 | title =  New BBN limits on physics beyond the standard model from He-4
 | journal = [[Astroparticle Physics]]
 | volume = 23 | issue = 3 | pages = 313–323
 | arxiv = astro-ph/0408033 | doi = 10.1016/j.astropartphys.2005.01.005
 | bibcode = 2005APh....23..313C | s2cid = 8210409
}}
</ref>
 
<ref name=Follin-Knox-Millea-Pan-2015>
{{cite journal
 |last1=Follin  |first1=Brent      |last2=Knox  |first2=Lloyd
 |last3=Millea  |first3=Marius     |last4=Pan   |first4=Zhen
 |year=2015
 |title=First detection of the acoustic oscillation phase shift expected from the cosmic neutrino background
 |journal=Physical Review Letters
 |volume=115  |issue=9  |page=091301
 |doi=10.1103/PhysRevLett.115.091301  |pmid=26371637
 |bibcode=2015PhRvL.115i1301F  |arxiv=1503.07863 |s2cid=24763212
}}
</ref>

<ref name=Gianpiero-etal-2005>
{{cite journal
 | first1 = Gianpiero | last1 = Mangano
 | display-authors=etal
 | year = 2005
 | title =  Relic neutrino decoupling including flavor oscillations
 | journal = Nuclear Physics 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 | s2cid = 18826928
}}
</ref>

<ref name=Komatsu-WMAP-etal-2011>
{{cite journal
 | first1 = Eiichiro | last1 = Komatsu
 | display-authors = etal
 | year = 2011
 | title =  Seven-year Wilkinson Microwave Anisotropy Probe (WMAP) observations: Cosmological interpretation
 | journal = The Astrophysical Journal Supplement Series
 | volume = 192 | issue = 2 | pages = 18
 | arxiv = 1001.4538  |bibcode = 2011ApJS..192...18K
 | doi = 10.1088/0067-0049/192/2/18  | s2cid = 17581520
}}
</ref>

<ref name=Long-Lunardn-Sabanclr-2014>
{{cite journal
 |last1=Cocco       |first1=A.G.
 |last2=Mangano  |first2=G. 
 |last3=Messina |first3=M.
 |year=2007
 |title=Probing low energy neutrino backgrounds with neutrino capture on beta decaying nuclei
 |journal=Journal of Cosmology and Astroparticle Physics
 |volume=0706 |issue=15 |page=082014
 |doi=10.1088/1742-6596/110/8/082014
|s2cid=16866395
 |doi-access=free|arxiv=hep-ph/0703075}}
</ref>

<ref name=Mangano-PTOLEMY-etal-2019>
{{cite journal
 |last1 = Mangano |first1 = Gianpiero
 |display-authors =etal
 |collaboration=PTOLEMY collaboration
 |year = 2019
 |title = Neutrino physics with the PTOLEMY project
 |journal = Journal of Cosmology and Astroparticle Physics
 |volume = 07  |page = 047
 |doi = 10.1088/1475-7516/2019/07/047
 |s2cid = 119397039 |arxiv = 1902.05508
}}
</ref>

}}  <!-- end "refs=" -->

{{Cosmology topics}}

[[Category:Cosmic background radiation]]
[[Category:Neutrino astronomy]]
[[Category:Physical cosmological concepts]]