The result of the Neutrino-4 experiment, sterile neutrinos and dark matter, the fourth neutrino and the Hubble constant

A brief analysis of the result of the Neutrino-4 experiment and the results of other experiments on the search for a sterile neutrino is presented. It is noted that a joint analysis of the results of the Neutrino-4 experiment and the data of the GALLEX, SAGE and BEST experiments confirms the parameters of neutrino oscillations declared by the Neutrino-4 experiment ($\Delta m^2_{14} = 7.3\text{eV}^2$ and $\sin^{2}2\theta_{14}\approx 0.36$) and increases the confidence level to $5.8{\sigma}$. An estimate of the contribution of sterile neutrinos with these parameters to the energy density of the Universe is made. It amounted to 5.3%. It is discussed that the extension of the neutrino model by introducing two more heavy sterile neutrinos in accordance with the number of types of active neutrinos will make it possible to explain the large-scale structure of the Universe and bring the contribution of sterile neutrinos to the dark matter of the Universe to the level of 27%. Possible contradictions between the measured sterile neutrino parameters and cosmological constraints are analyzed. It is shown that, based on modern astrophysical data, it is impossible to draw a definite conclusion in favor of the model of three or four neutrinos. It is noted that the introduction of the fourth neutrino removes the Hubble tension problem without contradictions with cosmic microwave background observed by the Planck collaboration. The influence of lepton asymmetry on the comparison of models of three or four neutrinos is considered. An estimate was made for the upper limit of the lepton asymmetry $L_e< 0.02$. The possibility of the appearance of lepton asymmetry due to CP violation during oscillations into sterile neutrinos is discussed.