# Cosmic neutrino background

The cosmic neutrino background (CNB[1]) is the universe's background particle radiation composed of neutrinos. They are sometimes known as relic neutrinos.

The CNB is a relic of the big bang; while the cosmic microwave background radiation (CMB) dates from when the universe was 379,000 years old, the CNB decoupled (separated) from matter when the universe was just one second old. It is estimated that today, the CNB has a temperature of roughly 1.95 K.

As neutrinos rarely interact with matter, these neutrinos still exist today. They have a very low energy, around 10−4 to 10−6 eV.[1] Even high energy neutrinos are notoriously difficult to detect, and the CνB has energies around 10−10 times smaller, so the CνB may not be directly observed in detail for many years, if at all.[1] However, Big Bang cosmology makes many predictions about the CνB, and there is very strong indirect evidence that the CνB exists.[1]

## Derivation of the CνB temperature

Given the temperature of the CMB, the temperature of the CνB 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 to approximately 2.5 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 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 neutrinos and the photons today. To find this ratio, we assume that the entropy of the universe was approximately conserved by the electron-positron annihilation. Then using

${\displaystyle \sigma \propto gT^{3},}$

where σ is the entropy, g is the effective degrees of freedom and T is the temperature, we find that

${\displaystyle \left({\frac {g_{0}}{g_{1}}}\right)^{\frac {1}{3}}={\frac {T_{1}}{T_{0}}},}$

where T0 denotes the temperature before the electron-positron annihilation and T1 denotes after. The factor g0 is determined by the particle species:

• 2 for photons, since they are massless bosons[2]
• 2 × (7/8) each for electrons and positrons, since they are fermions.[2]

g1 is just 2 for photons. So

${\displaystyle {\frac {T_{\nu }}{T_{\gamma }}}=\left({\frac {2}{2+2\times 7/8+2\times 7/8}}\right)^{\frac {1}{3}}=\left({\frac {4}{11}}\right)^{\frac {1}{3}}.}$

Given the current value of Tγ = 2.725 K,[3] it follows that Tν1.95 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 kTν falls below the rest mass energy mνc2. 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 ρR, typically parameterized in terms of the effective number of neutrino species Nν:

${\displaystyle \rho _{R}={\frac {\pi ^{2}}{15}}T_{\gamma }^{4}(1+z)^{4}\left[1+{\frac {7}{8}}N_{\nu }\left({\frac {4}{11}}\right)^{\frac {4}{3}}\right],}$

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 Nν3.046,[4] including a small correction caused by a non-thermal distortion of the spectra during e+-e-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 infer the value of Nν from observations.

### Big Bang nucleosynthesis

Due to its effect on the expansion rate of the universe during Big Bang nucleosynthesis (BBN), the theoretical expectations for the primordial abundances of light elements depend on Nν. Astrophysical measurements of the primordial 4
He
and 2
D
abundances lead to a value of Nν = 3.14+0.70
−0.65
at 68% c.l.,[5] 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 WMAP spacecraft's five-year data combined with type Ia supernova data and information about the baryon acoustic oscillation scale yielded Nν = 4.34+0.88
−0.86
at 68% c.l.,[6] providing an independent confirmation of the BBN constraints. The Planck spacecraft collaboration has published the tightest bound to date on the effective number of neutrino species, at Nν = 3.15±0.23.[7]

### Indirect evidence from phase changes to the Cosmic Microwave Background (CMB)

Big Bang cosmology makes many predictions about the CνB, 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 of the various CMB fluctuations.[1]

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 (1.96 ± 0.02K compared to a prediction of 1.95K), and exactly three types of neutrino, the same number of neutrino flavours currently predicted by the Standard Model.[1]

## Prospects for the direct detection of the CνB

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 CνB 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 CνB is to use capture of cosmic relic neutrinos on tritium i.e. ${\displaystyle ^{3}\mathrm {H} }$, leading to an induced form of beta decay.[8] The neutrinos of the CνB would lead to the production of electrons via the reaction ${\displaystyle \nu +{}^{3}\mathrm {H} \rightarrow {}^{3}\mathrm {He} +e^{-}}$, while the main background comes from electrons produced via natural beta decay ${\displaystyle ^{3}\mathrm {H} \rightarrow {}^{3}\mathrm {He} +e^{-}+{\bar {\nu }}}$. These electrons would be detected by the experimental apparatus in order to measure the size of the CνB. The latter source of electrons is far more numerous, however their maximum energy is smaller than the average energy of the CνB-electrons by twice the average neutrino mass. Since this mass is tiny, of the order of a few eVs 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 100g of tritium target.[9] Detector should be ready by 2022[10].

## Notes

1. ^ ν (italic ν) is the Greek letter nu, standardized symbol for neutrinos.

## References

1. Cosmic Neutrinos Detected, Confirming The Big Bang's Last Great Prediction - Forbes coverage of original paper: First Detection of the Acoustic Oscillation Phase Shift Expected from the Cosmic Neutrino Background - Follin, Knox, Millea, Pan, pub. Phys. Rev. Lett. 26 August 2015.
2. ^ a b Steven Weinberg (2008). Cosmology. Oxford University Press. p. 151. ISBN 978-0-19-852682-7.
3. ^ Fixsen, Dale; Mather, John (2002). "The Spectral Results of the Far-Infrared Absolute Spectrophotometer Instrument on COBE". Astrophysical Journal. 581 (2): 817–822. Bibcode:2002ApJ...581..817F. doi:10.1086/344402.
4. ^ Mangano, Gianpiero; et al. (2005). "Relic neutrino decoupling including flavor oscillations". Nucl. Phys. B. 729 (1–2): 221–234. arXiv:hep-ph/0506164. Bibcode:2005NuPhB.729..221M. doi:10.1016/j.nuclphysb.2005.09.041.
5. ^ Cyburt, Richard; et al. (2005). "New BBN limits on physics beyond the standard model from He-4". Astropart. Phys. 23 (3): 313–323. arXiv:astro-ph/0408033. Bibcode:2005APh....23..313C. doi:10.1016/j.astropartphys.2005.01.005.
6. ^ Komatsu, Eiichiro; et al. (2011). "Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation". The Astrophysical Journal Supplement Series. 192 (2): 18. arXiv:1001.4538. Bibcode:2011ApJS..192...18K. doi:10.1088/0067-0049/192/2/18.
7. ^ Ade, P.A.R.; et al. (2016). "Planck 2015 results. XIII. Cosmological parameters". Astron. Astrophys. 594 (A13): A13. arXiv:1502.01589. Bibcode:2016A&A...594A..13P. doi:10.1051/0004-6361/201525830.
8. ^ Long, A.J.; Lunardini, C.; Sabancilar, E. (2014). "Detecting non-relativistic cosmic neutrinos by capture on tritium: phenomenology and physics potential". JCAP. 1408 (8): 038. arXiv:1405.7654. Bibcode:2014JCAP...08..038L. doi:10.1088/1475-7516/2014/08/038.
9. ^ Betts, S.; et al. (2013). "Development of a Relic Neutrino Detection Experiment at PTOLEMY: Princeton Tritium Observatory for Light, Early-Universe, Massive-Neutrino Yield". arXiv:1307.4738 [astro-ph.IM].
10. ^ Mangano, Gianpiero; et al. (PTOLEMY collaboration) (2019). "Neutrino Physics with the PTOLEMY project". arXiv:1902.05508 [astro-ph.CO].