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Neutrino in Cosmology

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Abstract

Neutrinos play an important role in the evolution of Universe. High precision modern cosmological measurements are very important source of information of such neutrino properties as the number of neutrino flavors and the sum of neutrino masses. In this review we consider the basics of the cosmology (Friedman–Robertson–Walker metric, Friedman equations and their solutions, early Universe and neutrino decoupling, Big Bang Nucleosynthesis, Cosmic Microwave Background Radiation etc.), discuss the physical basis of the cosmological determination of neutrino properties and present latest value of the number of neutrino flavors and bounds on the sum of neutrino masses \(\sum\nolimits_i {{{m}_{i}}} \).

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Notes

  1. The cosmological principle was formulated by A. Einstein in 1917. At that time astrophysicists thought that the Universe is composed of stars. Evidence for the existence of Galaxies came later.

  2. 1 pc = \(3.26\,\,{\text{light}}\,\,{\text{years}} = 3.09 \times {{10}^{{16}}}{\kern 1pt} {\text{m}}\).

  3. From (56) and (58) follows that \({{\rho }_{c}} \simeq 0.86 \times {{10}^{{ - 26}}}\,\,{\text{kg}}\,\,{{{\text{m}}}^{{ - 3}}}\).

  4. In 2011 for discovery of the accelerating expansion of the Universe the Nobel Prize was awarded to S. Perlmutter, B. Schmidt and A. Riess.

  5. Notice that from analysis of cosmological data it was found [4] that \({{w}_{{mbda}}} = - 1.028(31)\).

  6. A condition for the thermal equilibrium in the expanding Universe we will discuss later.

  7. We use the following definition: \(\Delta m_{{ki}}^{2} = m_{i}^{2} - m_{k}^{2}\).

  8. Notice that stable nuclei heavier than \(^{{\text{7}}}{\text{Li}}\) in the BBN practically are not produced. It is connected with the fact that stable nuclei with atomic numbers 5 and 8 do not exist. This prevent production of nuclei heavier than \(^{{\text{7}}}{\text{Li}}\) in \(p + {{\,}^{4}}{\text{He}}\), \(^{{\text{4}}}{\text{He}} + {{\,}^{4}}{\text{He}}\) and other reactions.

  9. Notice that in the hydrogen recombination era helium atoms were not ionized (the ionization energy of helium is larger than that of hydrogen.)

  10.  For textbooks on the General Relativity see, for example, [27‒29].

  11.  In the same year D. Hilbert derived the equations of the General Relativity from a variational principle [30].

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  1. Joint Institute for Nuclear Research, R-141980, Dubna, Russia

    S. M. Bilenky

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Bilenky, S.M. Neutrino in Cosmology. Phys. Part. Nuclei 52, 337–356 (2021). https://doi.org/10.1134/S1063779621030035

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