The
cosmic neutrino background (CNB, CνB) is the universe's background particle radiation composed of
neutrinoA neutrino is an electrically neutral, weakly interacting elementary subatomic particle with a halfinteger spin, chirality and a disputed but small nonzero mass. It is able to pass through ordinary matter almost unaffected...
s.
Like the
cosmic microwave background radiationIn cosmology, cosmic microwave background radiation is thermal radiation filling the observable universe almost uniformly....
(CMB), the CνB is a relic of the
big bangThe Big Bang theory is the prevailing cosmological model that explains the early development of the Universe. According to the Big Bang theory, the Universe was once in an extremely hot and dense state which expanded rapidly. This rapid expansion caused the young Universe to cool and resulted in...
, and while the CMB dates from when the universe was 379,000 years old, the
CνB decoupledIn Big Bang cosmology, neutrino decoupling refers to the epoch at which neutrinos ceased interacting with baryonic matter, and thereby ceased influencing the dynamics of the universe at early times. Prior to decoupling, neutrinos were in thermal equilibrium with protons, neutrons, and electrons,...
from matter when the universe was 2 seconds old. It is estimated that today the CνB has a temperature of roughly . 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.
Derivation of the temperature of the CνB
Given the temperature of the CMB, the temperature of the CνB can be estimated. Before
neutrinos decoupledIn Big Bang cosmology, neutrino decoupling refers to the epoch at which neutrinos ceased interacting with baryonic matter, and thereby ceased influencing the dynamics of the universe at early times. Prior to decoupling, neutrinos were in thermal equilibrium with protons, neutrons, and electrons,...
from the rest of matter, the universe primarily consisted of neutrinos,
electronThe electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...
s,
positronThe positron or antielectron is the antiparticle or the antimatter counterpart of the electron. The positron has an electric charge of +1e, a spin of ½, and has the same mass as an electron...
s, and
photonIn physics, a photon is an elementary particle, the quantum of the electromagnetic interaction and the basic unit of light and all other forms of electromagnetic radiation. It is also the force carrier for the electromagnetic force...
s, all in
thermal equilibriumThermal equilibrium is a theoretical physical concept, used especially in theoretical texts, that means that all temperatures of interest are unchanging in time and uniform in space...
with each other. Once the temperature reached approximately , 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 annihilatedElectron–positron annihilation occurs when an electron and a positron collide. The result of the collision is the annihilation of the electron and positron, and the creation of gamma ray photons or, at higher energies, other particles:...
, 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 photons and the neutrinos 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 freedomIn statistics, the number of degrees of freedom is the number of values in the final calculation of a statistic that are free to vary.Estimates of statistical parameters can be based upon different amounts of information or data. The number of independent pieces of information that go into the...
and
T is the temperature, we find that
,
where
T denotes the temperature before the electronpositron annihilation and
T denotes after. To find
g , we add the degrees of freedom for electrons, positrons, and photons:
 2 for photons, since they are massless bosons
 2(7/8) each for electrons and positrons, since they are fermions
g is just 2 for photons. So
.
Given the current value of
T = , it follows that
T ≈ .
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 falls below the rest mass energy
mc. Instead, in this case one should rather track their energy density, which remains welldefined.
Indirect evidence for the CνB
Relativistic neutrinos contribute to the radiation energy density of the Universe
ρ, typically parameterized in terms of the effective number of neutrino species
N:
where
z denotes the
redshiftIn physics , redshift happens when light seen coming from an object is proportionally increased in wavelength, or shifted to the red end of the spectrum...
. The first term in the square brackets is due to the CMB, the second comes from the CνB. The
Standard ModelThe Standard Model of particle physics is a theory concerning the electromagnetic, weak, and strong nuclear interactions, which mediate the dynamics of the known subatomic particles. Developed throughout the mid to late 20th century, the current formulation was finalized in the mid 1970s upon...
with its three neutrino species predicts a value of
N ≃ , including a small correction caused by a nonthermal distortion of the spectra during
e^{+}The positron or antielectron is the antiparticle or the antimatter counterpart of the electron. The positron has an electric charge of +1e, a spin of ½, and has the same mass as an electron...

e^{}The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...

annihilationAnnihilation is defined as "total destruction" or "complete obliteration" of an object; having its root in the Latin nihil . A literal translation is "to make into nothing"....
. 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
inferInference is the act or process of deriving logical conclusions from premises known or assumed to be true. The conclusion drawn is also called an idiomatic. The laws of valid inference are studied in the field of logic.Human inference Inference is the act or process of deriving logical conclusions...
the value of
N from observations.
Big Bang Nucleosynthesis
Due to its effect on the
expansion rateThe metric expansion of space is the increase of distance between distant parts of the universe with time. It is an intrinsic expansion—that is, it is defined by the relative separation of parts of the universe and not by motion "outward" into preexisting space...
of the Universe during
Big Bang nucleosynthesisIn physical cosmology, Big Bang nucleosynthesis refers to the production of nuclei other than those of H1 during the early phases of the universe...
(BBN), the theoretical expectations for the primordial abundances of light elements depend on
N. Astrophysical measurements of the primordial and abundances lead to a value of
N = at 68%
c.l.In statistics, a confidence interval is a particular kind of interval estimate of a population parameter and is used to indicate the reliability of an estimate. It is an observed interval , in principle different from sample to sample, that frequently includes the parameter of interest, if the...
, 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
WMAPThe Wilkinson Microwave Anisotropy Probe — also known as the Microwave Anisotropy Probe , and Explorer 80 — is a spacecraft which measures differences in the temperature of the Big Bang's remnant radiant heat — the Cosmic Microwave Background Radiation — across the full sky. Headed by Professor...
spacecraft's fiveyear data combined with type Ia
SupernovaA supernova is a stellar explosion that is more energetic than a nova. It is pronounced with the plural supernovae or supernovas. Supernovae are extremely luminous and cause a burst of radiation that often briefly outshines an entire galaxy, before fading from view over several weeks or months...
data and information about the baryon acoustic oscillation scale yield
N = at 68% c.l., providing an independent confirmation of the BBN constraints. In the near future, probes such as the Planck spacecraft will likely improve present errors on
N by an order of magnitude.