Cosmic neutrino background

The cosmic neutrino background is that part of the background radiation of the universe that consists of neutrinos .

Like the cosmic microwave background , the cosmic neutrino background is a remnant of the Big Bang . In contrast to the cosmic microwave background, which was created around 380,000 years after the Big Bang, the neutrino background was created around 2 seconds after the Big Bang. It goes back to the decoupling of the neutrinos from the rest of the matter. The cosmic neutrino background is estimated to have a temperature of around 1.95 K today  .

Since neutrinos with a low energy only interact very weakly with matter, they are extremely difficult to detect. However, there is compelling indirect evidence of its existence. The planned experiment PTOLEMY aims to measure the neutrino background directly.

Derivation of the temperature

The temperature of  the neutrino background for massless neutrinos, which are always relativistic , can be estimated as follows, assuming the temperature of  the cosmic microwave background is given: ${\displaystyle T_{\nu }}$ ${\displaystyle T_{\gamma }}$

Before the neutrinos decoupled from the rest of the matter, the universe consisted primarily of neutrinos, electrons , positrons and photons , all of which were in thermal equilibrium with one another. When the temperature dropped to around 2.5 M eV (see natural units ), the neutrinos decoupled from the rest of the matter. Despite this decoupling, the neutrinos were still at the same temperature as the photons when the universe continued to expand. However, when the temperature dropped below the electron mass , most of the electrons and positrons were extinguished by pair annihilation . This transferred their energy and entropy to the photons, which corresponds to an increase in the temperature of the photon gas. The ratio of the temperatures  of neutrinos  and photons  in today's background radiation is the same as the ratio of the temperature of the photons before and after the electron-positron pair annihilation: ${\displaystyle T}$ ${\displaystyle \nu }$ ${\displaystyle \gamma }$

${\displaystyle {\frac {T_{\nu }}{T_{\gamma }}}={\frac {T_{0}}{T_{1}}}}$

where the index is intended to identify  one size before and the index  the same size after the electron-positron pair annihilation. ${\displaystyle _{0}}$ ${\displaystyle _{1}}$

To determine this relationship, we assume that the entropy of the universe is approximately preserved during the electron-positron pair annihilation: ${\displaystyle S}$

${\displaystyle S_{0}\approx S_{1}}$

With

${\displaystyle S\propto g\cdot T^{3}}$

in which

• ${\displaystyle g}$denote the effective number of degrees of freedom , determined by the type of particle:
  • 2  (7/8)for massless bosons , i.e. H. for photons
  • 2 · (7/8) for fermions , i.e. H. for leptons (electrons, positrons) and neutrinos.
• ${\displaystyle T}$the absolute temperature of the photon gas,

we receive

${\displaystyle \Rightarrow {\frac {T_{0}}{T_{1}}}=\left({\frac {g_{1}}{g_{0}}}\right)^{1/3}}$

So:

${\displaystyle {\frac {T_{\nu }}{T_{\gamma }}}={\frac {T_{0}}{T_{1}}}=\left({\frac {2}{2+2\cdot {\frac {7}{8}}+2\cdot {\frac {7}{8}}}}\right)^{1/3}=\left({\frac {4}{11}}\right)^{1/3}}$

With today's value for the temperature of the cosmic microwave background follows ${\displaystyle T_{\gamma }=2{,}725\,\mathrm {K} }$

${\displaystyle T_{\nu }\approx 1{,}95\,\mathrm {K} }$.

For neutrinos with a mass other than zero , the temperature approach is no longer suitable as soon as they become non-relativistic. This happens when their thermal energy falls below their rest energy . In this case, it is better to consider the energy density , which is still well-defined. ${\displaystyle 3/2\cdot k\cdot T_{\nu }}$ ${\displaystyle m_{\nu }\cdot c^{2}}$

Indirect evidence

Relativistic neutrinos contribute to the radiation density of the universe: ${\displaystyle \rho _{\rm {R}}}$

${\displaystyle \rho _{\rm {R}}={\frac {\pi ^{2}}{15}}\,T_{\gamma }^{4}(1+z)^{4}\left[1+{\frac {7}{8}}N_{\rm {\nu }}\left({\frac {4}{11}}\right)^{4/3}\right]}$

With

• the redshift  ${\displaystyle z}$
• the effective number  of neutrino generations . ${\displaystyle N_{\nu }}$

The first term in square brackets describes the cosmic microwave background, the second the cosmic neutrino background. The standard model of elementary particle physics predicts the effective value with its three neutrino types. ${\displaystyle N_{\nu }\approx 3{,}046}$

Primordial nucleosynthesis

Since the effective number of neutrino genera affects the expansion speed of the universe during primordial nucleosynthesis , the theoretically expected values ​​for the primordial frequencies of light elements depend on it. Astrophysical measurements of the primordial abundances of helium -4 and deuterium lead to a value of at a confidence level of 68%, which is in agreement with the expectation from the Standard Model. ${\displaystyle N_{\nu }=3{,}14_{-0{,}65}^{+0{,}70}}$

Anisotropies in the cosmic background radiation and structure formation

The presence of the cosmic neutrino background influences both the development of anisotropies in the cosmic background radiation and the growth of density fluctuations in two ways:

• on the one hand through its contribution to the radiation density of the universe (which, for example, determines the point in time of the transition from radiation to matter-dominated universe),
• on the other hand through the anisotropic pressure, which dampens the baryonic acoustic vibrations .

In addition, massive neutrinos that freely propagate suppress structure formation on small length scales. The five-year data acquisition of the WMAP satellite in combination with data on type I supernovae and information on the strength of the baryonic acoustic oscillations yield a value of at a confidence level of 68%, which is an independent confirmation of the limits for primordial nucleosynthesis. In the near future, studies like those of the Planck Space Telescope are expected to reduce the current uncertainties by an order of magnitude. ${\displaystyle N_{\nu }=4{,}34_{-0{,}86}^{+0{,}88}}$ ${\displaystyle N_{\nu }}$ ${\displaystyle N_{\nu }}$

Individual evidence

1. ↑ S. Betts u. a .: Development of a Relic Neutrino Detection Experiment at PTOLEMY: Princeton Tritium Observatory for Light, Early-Universe, Massive-Neutrino Yield . August 26, 2013, arxiv : 1307.4738 .
2. ↑ Steven Weinberg: Cosmology . Oxford University Press, 2008, ISBN 978-0-19-852682-7 , pp. 151 .
3. ↑ Dale Fixsen, Mather, John: The Spectral Results of the Far-Infrared Absolute Spectrophotometer instrument on COBE . In: Astrophysical Journal . 581, No. 2, 2002, pp. 817-822. bibcode : 2002ApJ ... 581..817F . doi : 10.1086 / 344402 .
4. ↑ Gianpiero Mangano, et al .: Relic neutrino decoupling including flavor oscillations . In: Nucl.Phys.B . 729, No. 1-2, 2005, pp. 221-234. arxiv : hep-ph / 0506164 . bibcode : 2005NuPhB.729..221M . doi : 10.1016 / j.nuclphysb.2005.09.041 .
5. ↑ Richard Cyburt, et al .: New BBN limits on physics beyond the standard model from He-4 . In: Astropart.Phys. . 23, No. 3, 2005, pp. 313-323. arxiv : astro-ph / 0408033 . bibcode : 2005APh .... 23..313C . doi : 10.1016 / j.astropartphys.2005.01.005 .
6. ↑ Eiichiro Komatsu, et al .: Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation . In: The Astrophysical Journal Supplement Series . 192, No. 2, 2010, p. 18. arxiv : 1001.4538 . bibcode : 2011ApJS..192 ... 18K . doi : 10.1088 / 0067-0049 / 192/2/18 .
7. ↑ Sergej Bashinsky, Seljak, Uroš: Neutrino perturbations in CMB anisotropy and matter clustering . In: Phys.Rev.D . 69, No. 8, 2004, p. 083002. arxiv : astro-ph / 0310198 . bibcode : 2004PhRvD..69h3002B . doi : 10.1103 / PhysRevD.69.083002 .