Neutrino and Cosmology

Neutrinos are, with the photons, the most abundant particles in the Universe. In the big bang theory (the “standard” model of the Universe), light neutrinos have thermally decoupled from the other forms of matter (quarks and leptons) approximately 1 second after the big bang, when the temperature decreased to about  1010 K (~ MeV). They constitute the cosmic neutrino background, the first witnesses still alive of the big bang (the photon background, the so-called cosmic microwave background (CMB), is “younger” since the decoupling took place 380 000 years later). Their temperature has now decreased to 1.95 K and their density (all the species together) is presently 330 neutrinos per cm3.

The energy of these relic neutrinos is so low (mean energy of ~0.1 meV) that their cross section is very small (order of 10-60 cm2) and it has not yet been possible to detect them. Some hope to detect relic neutrinos emerged when it was realized that coherent interaction can enhance the cross section. Indeed these low energy neutrinos have a macroscopic de Broglie wave length (≈ 0.5 mm). Several ingeneous ideas has been proposed since more than 50 years (see the review by Gelmini in 2004 [Gel04]) :

  1. – mechanical momentun transfer on macroscopic object [Oph74, Lew80], but this simple idea was shown to be highly reduced at the level of GF2 [Cab82]
  2. – torque on a ferromagnetic plate [Sto75]
  3. – torsion balance to measure the mechanical force exerted by elastic scattering of cosmic neutrinos on macroscopic targets [Hag99]

Steven Weinberg proposed in 1962 to look for the signal for relic neutrino capture on tritium [Wei62]. Raghavan revised this idea [Rag07] and  today the Ptolemy collaboration [Bet13] is making the first steps toward its experimental realization.

It is also worth noticing that the interaction of (still undiscovered) ultra-high energy neutrinos (~ 1021 eV) with the relic neutrinos to produce a Z0, signed by a huge increase in the cross section [Wei82] (see [Rin01] for a recent review).

If no direct method has proved the existence of the relic neutrinos, there are indirect approaches which give confidence that they really exist:

  1. the big bang nucleosynthesis, which generates the light nuclei (D, 3He, 4He, 7Li) [Wag67], asks for a number of neutrino species smaller than 5 [Ste77].
  2. the cosmic neutrino background affects the evolution of CMB anisotropies and the structure formation in the Universe. The last results of the Planck satellite also require a number of neutrinos close to 3 [Ade13]; in addition, Planck and other cosmological experiments give a very constraining upper limit on the mass of the neutrinos.

Neutrinos as dark matter candidates ?

Since the works of Zwicky in 1933 and Rubin in 1970, we know that some “dark matter”, observed only through its gravitational interaction, is present in the universe and is about 6 times more abundant than the visible matter. As soon as the solar neutrino deficit was supposed to be the consequence of neutrino oscillation and that neutrinos are thus massive, physicists, knowing that there are many neutrinos (about 330 per cm3) of cosmological origin, proposed that neutrinos could be the main component of the dark matter. But, it required the neutrino mass to be at least of 10 eV. The lastest results on the neutrino oscillation parameters and the strong cosmological constraints on the neutrino mass provided by experiments like Planck have excluded this hypothesis and the hope to have found a good candidate for the dark matter.

The idea that a fourth neutrino which would be massive (~keV) and sterile has been popular in the recent years. We need more experimental proofs before considering that they could constitute part of dark matter.

Further information

During the conference on the History of the Neutrino (Sept. 5-7, 2018 in Paris) the subject of history of Neutrinos in Cosmology was reviewed by James Rich (CEA Saclay, France) : here the slides , the video of his talk and his contribution to the Proceedings.


Ade13P.A.R. Ade et al. Planck 2013 Results. XVI. Cosmological Parameters Astronomy and Astrophysics 571 (2014) A16; arXiv:1303.5076
Bet13S. Betts et al. Development of a relic neutrino detection experiment at PTOLEMY arXiv:1307.4738
Cab82N. Cabibbo and L. MaianiThe Vanishing of order-G Mechanical Effects of Cosmic Massive Neutrinos on Bulk MatterPhys. Lett. B114 (1982) 115
Gel04G. Gelmini Prospect for relic neutrino search arXiv:hep-ph/0412305
Hag99C. HagmannCosmic neutrinos and their detectionarXiv:astro-ph/9905258
Lan83P. LangackerOn the detection of cosmological neutrinos by coherent scatteringPhys. Rev. D27 (1983) 1228
Lew80R.R. LewisCoherent detector for low-energy neutrinosPhys. Rev. D21 (1980) 663
Oph74R.OpherCoherent Scattering of Cosmic NeutrinosAstron. & Astrophys. 37 (1974) 135
Rag07R.S. RaghavanZero Threshold Reactions for Detecting Ultra Low Energy Cosmic Relic NeutrinosarXiv:hep-ph/0703028
Rin01A. RingwaldPossible detection of relic neutrinos and their massarXiv:hep-ph/0111112
Ste77Gary Steigman, David N. Schramm and James E. Gunn Cosmological limits to the number of massive leptonsPhys. Lett. B66 (1977) 202
Sto75L. Stodolsky Speculations on Detection of the “Neutrino Sea” Phys. Rev. Lett. 34 (1975) 110
Wag67R.V. Wagoner, W.A. Fowler, F. HoyleOn the synthesis of elements at very high temperaturesThe Astrophysical Journal 148 (1967) 3
Wei62S. Weinberg Universal neutrino degeneracy Phys. Rev. 128 (1962) 1457
Wei82T. WeilerResonant absorption of cosmic-ray neutrinos by the relic-neutrino backgroundPhys. Rev. Lett. 49 (1982) 234

2 thoughts on “Neutrino and Cosmology”

  1. Je ne suis pas sûr que je dirais que les résultats sur les oscillations ont exclu la possibilité que les neutrinos constituent la matière noire, car elles ne contraignent que les Delta m^2. C’est plutôt, côté cosmo, la formation des structures (qui défavorise la matière noire chaude), et côté physique des particules, la limite cinématique sur la masse effective mesurée dans la désintégration bêta. Ensuite, les mesures cosmologiques de précision (WMAP, Planck) ont mis une limite de plus en plus forte sur les masses des neutrinos.

  2. Cette section efficace de 10-60 cm2 me surprends :
    – si X-section ≈ (GFxE_nu)^2 => ≈ 10-63 cm2.
    Il me semblait avoir lu que si les neutrinos sont massifs la section efficace arrivait à un plateau à
    ≈ (GFxm_nu)^2 ≈ 2×10-60 cm2 pour m_nu ≈ 8 meV
    ≈ 86×10-60 cm2 pour m_nu ≈ 50 meV

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