Cosmic neutrino background
Encyclopedia
The cosmic neutrino background (CNB, CνB) is the universe's background particle radiation composed of neutrino
s.
Like the cosmic microwave background radiation
(CMB), the CνB is a relic of the big bang
, and while the CMB dates from when the universe was 379,000 years old, the CνB decoupled
from matter when the universe was 2 seconds old. It is estimated that today the CνB has a temperature of roughly . Since low-energy 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.
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 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 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 photons and the neutrinos today. To find this ratio, we assume that the entropy of the universe was approximately conserved by the electron-positron 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 denotes the temperature before the electron-positron annihilation and T denotes after. To find g , we add the degrees of freedom for electrons, positrons, and photons:
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 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 kT falls below the rest mass energy mc. Instead, in this case one should rather track their energy density, which remains well-defined.
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 ≃ , 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 N from observations.
of the Universe during Big Bang nucleosynthesis
(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 very good agreement with the Standard Model expectation.
spacecraft's five-year data combined with type Ia Supernova
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.
Neutrino
A neutrino is an electrically neutral, weakly interacting elementary subatomic particle with a half-integer spin, chirality and a disputed but small non-zero mass. It is able to pass through ordinary matter almost unaffected...
s.
Like the cosmic microwave background radiation
Cosmic microwave background radiation
In cosmology, cosmic microwave background radiation is thermal radiation filling the observable universe almost uniformly....
(CMB), the CνB is a relic of the big bang
Big Bang
The 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 decoupled
Neutrino decoupling
In 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 low-energy 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 decoupledNeutrino decoupling
In 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, electron
Electron
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...
s, positron
Positron
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...
s, and photon
Photon
In 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 equilibrium
Thermal equilibrium
Thermal 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 annihilated
Electron-positron annihilation
Electron–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 electron-positron 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 electron-positron annihilation. Then using
,where σ is the entropy, g is the effective degrees of freedom
Degrees of freedom (statistics)
In 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 electron-positron 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 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 kT falls below the rest mass energy mc. 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 ρ, typically parameterized in terms of the effective number of neutrino species N:where z denotes the redshift
Redshift
In 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 Model
Standard Model
The 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 non-thermal distortion of the spectra during e+
Positron
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-
Electron
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...
-annihilation
Annihilation
Annihilation 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 infer
Inference
Inference 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 rateMetric expansion of space
The 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 nucleosynthesis
Big Bang nucleosynthesis
In physical cosmology, Big Bang nucleosynthesis refers to the production of nuclei other than those of H-1 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.
Confidence interval
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 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 WMAPWilkinson Microwave Anisotropy Probe
The 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 five-year data combined with type Ia Supernova
Supernova
A 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.