Cosmic neutrino background

The cosmic neutrino background (CνB) is the universe's background particle radiation composed of neutrino

Neutrino

Neutrinos are elementary particles that often travel close to the speed of light, lack an electric charge, are able to pass through ordinary matter almost undisturbed and are thus extremely difficult to detect. Neutrinos have a minuscule, but nonzero mass...

s.

Like the cosmic microwave background radiation

Cosmic microwave background radiation

In cosmology, cosmic microwave background radiation is a form of electromagnetic radiation filling the universe. With a traditional optical telescope, the space between stars and galaxies is pitch black...

 (CMB), the CνB is a relic of the big bang

Big Bang

The Big Bang is the cosmological model of the initial conditions and subsequent development of the Universe that is supported by the most comprehensive and accurate explanations from current scientific evidence and observation...

, and while the CMB dates from when the universe was 380,000 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 1.95 K. 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 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 the rest of matter, the universe primarily consisted of neutrinos, electrons, positrons and photons, all in thermal equilibrium with each other. Once the temperature reached approximately 1 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

Electron-positron annihilation

Electron–positron annihilation occurs when an electron and a positron collide. The result of the collision is the conversion of the electron and positron and the creation of gamma ray photons or, less often, other particles. The process must satisfy a number of conservation laws, including:*...

, 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 is the entropy, is the effective number of degrees of freedom

Degrees of freedom

Degrees of freedom can mean:* Degrees of freedom * Degrees of freedom * Degrees of freedom...

 and is the temperature, we find that
,

where the subscript 0 denotes before the electron-positron annihilation and 1 denotes after. To find , 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

is just 2 for photons. So
.

Given the current value of , it follows that .

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 falls below the rest mass energy . 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 _R, typically parameterized in terms of the effective number of neutrino species _ν:
where denotes the redshift

Redshift

In physics and astronomy, redshift occurs when electromagnetic radiation—usually visible light—emitted or reflected by an object is shifted towards the red end of the electromagnetic spectrum due to the Doppler effect or other gravitationally-induced effects...

. 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 of three of the four known fundamental interactions and the elementary particles that take part in these interactions. These particles make up all visible matter in the universe...

 with its three neutrino species predicts a value of , 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 +1, a spin of , and the same mass as an electron. When a low-energy positron collides with a low-energy electron, annihilation occurs, resulting in the production...

-e^-

Electron

An electron is a subatomic particle that carries a negative electric charge. It has no known substructure and is believed to be a point particle. An electron has a mass that is approximately 1836 times less than that of the proton. The intrinsic angular momentum of the electron is a half integer...

-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

An inference is an assumption of what will happen rather than a true conclusion, prediction or hypothesis.* Human inference is traditionally studied within the field of cognitive psychology....

 the value of from observations.

Big Bang Nucleosynthesis

Due to its effect on the expansion rate

Metric expansion of space

The metric expansion of space is the averaged increase of metric distance between distant objects in 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 . Astrophysical measurements of the primordial ⁴He

Helium

Helium is the chemical element with atomic number 2, and is represented by the symbol He. It is a colorless, odorless, tasteless, non-toxic, inert monatomic gas that heads the noble gas group in the periodic table...

 and Deuterium

Deuterium

Deuterium, also called heavy hydrogen, is a stable isotope of hydrogen with a natural abundance in the oceans of Earth of approximately one atom in of hydrogen...

 abundances lead to a value of at 68% c.l.

Confidence interval

In statistics, a confidence interval is a particular kind of interval estimate of a population parameter. Instead of estimating the parameter by a single value, an interval likely to include the parameter is given. Thus, confidence intervals are used to indicate the reliability of an estimate...

, 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

Wilkinson 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...

 satellite's five-year data combined with type Ia Supernova

Supernova

A supernova is a stellar explosion. 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. During this short interval, a supernova can radiate as much energy as the Sun could emit over...

 data and information about the baryon acoustic oscillation scale yield at 68% c.l., providing an independent confirmation of the BBN constraints. In the near future, probes such as the Planck satellite will likely improve present errors on by an order of magnitude.