Cosmic neutrino background
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The cosmic neutrino background (CNB, CνB^{[1]}) is the universe's background particle radiation composed of neutrinos. They are sometimes known as relic neutrinos.
Like the cosmic microwave background radiation (CMB), the CνB is a relic of the big bang; while the CMB dates from when the universe was 379,000 years old, the CνB decoupled from matter when the universe was two seconds old. It is estimated that today, the CνB has a temperature of roughly K. Since lowenergy 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 indirect evidence for its existence. 1.95
Contents
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 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 2.5 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 electronpositron 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 electronpositron annihilation. Then using
 ,
where σ is the entropy, g is the effective degrees of freedom and T is the temperature, we find that
 ,
where T_{0} denotes the temperature before the electronpositron annihilation and T_{1} denotes after. The factor g_{0} is determined by the particle species:
 2 for photons, since they are massless bosons^{[1]}
 2×(7/8) each for electrons and positrons, since they are fermions.^{[1]}
g_{1} is just 2 for photons. So
 .
Given the current value of T_{γ} = ,^{[2]} it follows that T_{ν} ≈ 2.725 K. 1.95 K
The above discussion is valid for massless neutrinos, which are always relativistic. For neutrinos with a nonzero rest mass, the description in terms of a temperature is no longer appropriate after they become nonrelativistic; i.e., when their thermal energy 3/2 kT_{ν} falls below the rest mass energy m_{ν}c^{2}. Instead, in this case one should rather track their energy density, which remains welldefined.
Indirect mathematical evidence for the CνB
Relativistic neutrinos contribute to the radiation energy density of the universe ρ_{R}, typically parameterized in terms of the effective number of neutrino species N_{ν}:
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_{ν} ≃ ,^{[3]} including a small correction caused by a nonthermal distortion of the spectra during 3.046e^{+}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 N_{ν} 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 N_{ν}. Astrophysical measurements of the primordial 4He and 2D abundances lead to a value of N_{ν} = +0.70
−0.65 at 68% 3.14c.l.,^{[4]} 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 matterradiation equality), and due to the neutrinos' anisotropic stress which dampens the acoustic oscillations of the spectra. Additionally, freestreaming massive neutrinos suppress the growth of structure on small scales. The WMAP spacecraft's fiveyear data combined with type Ia supernova data and information about the baryon acoustic oscillation scale yield N_{ν} = +0.88
−0.86 at 68% c.l.,^{[5]} providing an independent confirmation of the BBN constraints. In the near future, probes such as the 4.34Planck spacecraft will likely improve present errors on N_{ν} by an order of magnitude.^{[6]}
See also
Notes
References
 ↑ ^{1.0} ^{1.1} Steven Weinberg (2008). Cosmology. Oxford University Press. p. 151. ISBN 9780198526827.
 ↑ Fixsen, Dale; Mather, John (2002). "The Spectral Results of the FarInfrared Absolute Spectrophotometer Instrument on COBE". Astrophysical Journal. 581 (2): 817–822. Bibcode:2002ApJ...581..817F. doi:10.1086/344402.
 ↑ Mangano, Gianpiero; et al. (2005). "Relic neutrino decoupling including flavor oscillations". Nucl.Phys.B. 729 (1–2): 221–234. Bibcode:2005NuPhB.729..221M. arXiv:hepph/0506164 . doi:10.1016/j.nuclphysb.2005.09.041.
 ↑ Cyburt, Richard; et al. (2005). "New BBN limits on physics beyond the standard model from He4". Astropart.Phys. 23 (3): 313–323. Bibcode:2005APh....23..313C. arXiv:astroph/0408033 . doi:10.1016/j.astropartphys.2005.01.005.
 ↑ Komatsu, Eiichiro; et al. (2010). "SevenYear Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation". The Astrophysical Journal Supplement Series. 192 (2): 18. Bibcode:2011ApJS..192...18K. arXiv:1001.4538 . doi:10.1088/00670049/192/2/18.
 ↑ Bashinsky, Sergej; Seljak, Uroš (2004). "Neutrino perturbations in CMB anisotropy and matter clustering". Phys. Rev. D. 69 (8): 083002. Bibcode:2004PhRvD..69h3002B. arXiv:astroph/0310198 . doi:10.1103/PhysRevD.69.083002.