title: ÐÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ðµ Ð½ÐµÐ¹ÑÑÐ¸Ð½Ð½ÑÑ ÑÐ¿ÐµÐºÑÑÐ¾Ð² Ð¾Ñ Ð¿ÐµÑÐ²Ð¸ÑÐ½ÑÑ ÑÐµÑÐ½ÑÑ Ð´ÑÑ
title: Ð²ÑÐ¿ÑÑÐºÐ½Ð°Ñ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð¼Ð°Ð³Ð¸ÑÑÑÐ°
titleType: Subtitle
title: Research on neutrino spectra from primordial black holes
Creators: name: ÐÑÑÑÐ¹, Ð®Ð»Ð¸Ð°Ð½
Publisher: name: Ð¡Ð°Ð½ÐºÑ-ÐÐµÑÐµÑÐ±ÑÑÐ³ÑÐºÐ¸Ð¹ Ð¿Ð¾Ð»Ð¸ÑÐµÑÐ½Ð¸ÑÐµÑÐºÐ¸Ð¹ ÑÐ½Ð¸Ð²ÐµÑÑÐ¸ÑÐµÑ ÐÐµÑÑÐ° ÐÐµÐ»Ð¸ÐºÐ¾Ð³Ð¾
Year: 2024
Subjects: Ð§ÐµÑÐ½ÑÐµ Ð´ÑÑÑ (Ð°ÑÑÑÐ¾Ð½.)
ÐÐµÐ¹ÑÑÐ¸Ð½Ð¾
Ð¸Ð·Ð»ÑÑÐµÐ½Ð¸Ðµ Ð¥Ð¾ÐºÐ¸Ð½Ð³Ð°
Ð»Ð¾Ð³Ð½Ð¾ÑÐ¼Ð°Ð»ÑÐ½Ð¾Ðµ ÑÐ°ÑÐ¿ÑÐµÐ´ÐµÐ»ÐµÐ½Ð¸Ðµ
ÑÐ¿ÐµÐºÑÑ Ð¼Ð°ÑÑ
ÑÐ²Ð¾Ð»ÑÑÐ¸Ñ ÐÑÐµÐ»ÐµÐ½Ð½Ð¾Ð¹
Ð¿Ð°ÑÐ°Ð¼ÐµÑÑ Ð¥Ð°Ð±Ð±Ð»Ð°
Hawking radiation
mass spectrum
log-normal distribution
evolution of the universe
Hubble parameter

description: ÐÐ°Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð¿Ð¾ÑÐ²ÑÑÐµÐ½Ð° Ð¼Ð½Ð¾Ð¶ÐµÑÑÐ²ÐµÐ½Ð½Ð¾Ð¼Ñ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ ÑÐ½ÐµÑÐ³ÐµÑÐ¸ÑÐµÑÐºÐ¸Ñ ÑÐ¿ÐµÐºÑÑÐ¾Ð² Ð½ÐµÐ¹ÑÑÐ¸Ð½Ð¾, ÑÐ¾Ð¶Ð´Ð°ÑÑÐ¸ÑÑÑ Ð² ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÐµ Ð¸ÑÐ¿Ð°ÑÐµÐ½Ð¸Ñ Ð¿ÐµÑÐ²Ð¸ÑÐ½ÑÑ ÑÐµÑÐ½ÑÑ Ð´ÑÑ (ÐÐ§Ð), ÐºÐ¾ÑÐ¾ÑÑÐµ Ð¾Ð´Ð½Ð¾ÑÐ¾Ð´Ð½Ð¾ ÑÐ°ÑÐ¿ÑÐµÐ´ÐµÐ»ÐµÐ½Ñ Ð¿Ð¾ ÐÑÐµÐ»ÐµÐ½Ð½Ð¾Ð¹ Ñ Ð»Ð¾Ð³Ð½Ð¾ÑÐ¼Ð°Ð»ÑÐ½ÑÐ¼ ÑÐ¿ÐµÐºÑÑÐ¾Ð¼ Ð¸Ñ Ð¼Ð°ÑÑ. Ð¦ÐµÐ»Ñ ÑÐ°Ð±Ð¾ÑÑ -- Ð¾Ð¿ÑÐµÐ´ÐµÐ»Ð¸ÑÑ ÑÐ°ÐºÐ¸Ðµ Ð¿Ð°ÑÐ°Ð¼ÐµÑÑÑ $\sigma, M_{\mathrm{c}}$ ÑÐ¿ÐµÐºÑÑÐ° Ð¼Ð°ÑÑ, Ð¿ÑÐ¸ ÐºÐ¾ÑÐ¾ÑÑÑ ÑÑÐ¼Ð¼Ð°ÑÐ½ÑÐµ Ð¿Ð¾ÑÐ¾ÐºÐ¸ Ð½ÐµÐ¹ÑÑÐ¸Ð½Ð¾ Ð±ÑÐ´ÑÑ Ð´Ð¾ÑÑÐ°ÑÐ¾ÑÐ½Ð¾ Ð²ÐµÐ»Ð¸ÐºÐ¸, ÑÑÐ¾Ð±Ñ Ð¸Ñ Ð¼Ð¾Ð¶Ð½Ð¾ Ð±ÑÐ»Ð¾ Ð¾Ð´Ð½Ð¾Ð·Ð½Ð°ÑÐ½Ð¾ Ð¸Ð´ÐµÐ½ÑÐ¸ÑÐ¸ÑÐ¸ÑÐ¾Ð²Ð°ÑÑ, ÐºÐ¾ÑÐ²ÐµÐ½Ð½Ð¾ Ð¿Ð¾Ð´ÑÐ²ÐµÑÐ´Ð¸Ð² Ð½Ð°Ð»Ð¸ÑÐ¸Ðµ ÐÐ§Ð Ð²Ð¾ ÐÑÐµÐ»ÐµÐ½Ð½Ð¾Ð¹; Ð¾ÑÐµÐ½Ð¸ÑÑ Ð²Ð»Ð¸ÑÐ½Ð¸Ðµ ÑÐ½ÐµÑÐ³ÐµÑÐ¸ÑÐµÑÐºÐ¾Ð³Ð¾ Ð²ÐºÐ»Ð°Ð´Ð° Ð½ÐµÐ¹ÑÑÐ¸Ð½Ð¾ Ð¾Ñ ÐÐ§Ð Ð½Ð° ÑÐµÐ¼Ð¿ ÑÐ°ÑÑÐ¸ÑÐµÐ½Ð¸Ñ ÐÑÐµÐ»ÐµÐ½Ð½Ð¾Ð¹. ÐÐµÑÐ¾Ð´ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ Ð²ÐºÐ»ÑÑÐ°ÐµÑ Ð² ÑÐµÐ±Ñ ÑÐ¸Ð¼ÑÐ»ÑÑÐ¸Ñ Ð¶Ð¸Ð·Ð½Ð¸ ÐÐ§Ð, Ð¿Ð¾Ð»ÑÑÐµÐ½Ð¸Ðµ Ð¸ Ð°Ð½Ð°Ð»Ð¸Ð· ÑÑÐ¼Ð¼Ð°ÑÐ½ÑÑ Ð´Ð¸ÑÑÐµÑÐµÐ½ÑÐ¸Ð°Ð»ÑÐ½ÑÑ Ð¿Ð¾ÑÐ¾ÐºÐ¾Ð² Ð²ÑÐµÑ ÑÐ¸Ð¿Ð¾Ð² Ð½ÐµÐ¹ÑÑÐ¸Ð½Ð¾ Ñ ÑÑÐµÑÐ¾Ð¼ Ð¶ÐµÑÑÐºÐ¸Ñ Ð¾Ð³ÑÐ°Ð½Ð¸ÑÐµÐ½Ð¸Ð¹ Ð½Ð° ÑÐ°ÑÐ¿ÑÐ¾ÑÑÑÐ°Ð½ÐµÐ½Ð½Ð¾ÑÑÑ ÐÐ§Ð Ð¸ ÐºÐ¾ÑÐ¼Ð¾Ð»Ð¾Ð³Ð¸ÑÐµÑÐºÐ¾Ð³Ð¾ ÐºÑÐ°ÑÐ½Ð¾Ð³Ð¾ ÑÐ¼ÐµÑÐµÐ½Ð¸Ñ $z$ Ð¿ÑÐ¸ ÑÐ°Ð·Ð»Ð¸ÑÐ½ÑÑ Ð¿Ð°ÑÐ°Ð¼ÐµÑÑÐ°Ñ, Ð¿Ð¾Ð¸ÑÐº Ð¼Ð°ÐºÑÐ¸Ð¼Ð°Ð»ÑÐ½ÑÑ Ð¿Ð¾ ÑÐ½ÐµÑÐ³ÐµÑÐ¸ÐºÐµ Ð¿Ð¾ÑÐ¾ÐºÐ¾Ð² Ð¸ ÑÑÐµÑ Ð²Ð»Ð¸ÑÐ½Ð¸Ñ Ð¿Ð»Ð¾ÑÐ½Ð¾ÑÑÐ¸ Ð¸Ñ ÑÐ½ÐµÑÐ³Ð¸Ð¹ Ð½Ð° Ð¿Ð°ÑÐ°Ð¼ÐµÑÑ Ð¥Ð°Ð±Ð±Ð»Ð° $H(z)$. Ð ÐµÐ·ÑÐ»ÑÑÐ°ÑÑ Ð¿Ð¾ÐºÐ°Ð·ÑÐ²Ð°ÑÑ, ÑÑÐ¾ Ð½Ð°Ð¸Ð±Ð¾Ð»ÐµÐµ Ð±Ð»Ð°Ð³Ð¾Ð¿ÑÐ¸ÑÑÐ½ÑÐµ Ð¿Ð°ÑÐ°Ð¼ÐµÑÑÑ Ð´Ð»Ñ ÑÐµÐ³Ð¸ÑÑÑÐ°ÑÐ¸Ð¸ Ð½ÐµÐ¹ÑÑÐ¸Ð½Ð¾ Ð¾Ñ ÐÐ§Ð Ð½Ð°ÑÐ¾Ð´ÑÑÑÑ Ð² ÑÐ·ÐºÐ¾Ð¼ Ð½Ð¸Ð·ÐºÐ¾ÑÐ½ÐµÑÐµÐ³Ð¸ÑÐ¸ÑÐ½Ð¾Ð¼ Ð´Ð¸Ð°Ð¿Ð°Ð·Ð¾Ð½Ðµ $10^{-8} - 10^{-5}$~ÐÑÐ Ð¿ÑÐ¸ Ð¼ÐµÐ´Ð¸Ð°Ð½Ð½ÑÑ Ð¼Ð°ÑÑÐ°Ñ $10^{8}\:\text{Ð³} \lesssim M_{\mathrm{c}} \lesssim 10^{11}$ Ð³ Ð¸ ÑÐ¸ÑÐ¸Ð½Ðµ $0 \lesssim \sigma \lesssim 3.0$. ÐÐ°ÐºÑÐ¸Ð¼Ð°Ð»ÑÐ½ÑÐ¹ ÑÐ½ÐµÑÐ³ÐµÑÐ¸ÑÐµÑÐºÐ¸Ð¹ Ð²ÐºÐ»Ð°Ð´ Ð²Ð½Ð¾ÑÑÑ Ð½ÐµÐ¹ÑÑÐ¸Ð½Ð¾ Ð¾Ñ ÐÐ§Ð ÑÐ°ÑÐ¿ÑÐµÐ´ÐµÐ»ÐµÐ½Ð¸Ñ Ñ $M_{\mathrm{c}} = 2.4 \times 10^{9}$ Ð³ Ð¸ $\sigma \approx 2.8$, Ð¿ÑÐ¸ ÐºÐ¾ÑÐ¾ÑÑÑ Ð¾ÑÐ½Ð¾ÑÐ¸ÑÐµÐ»ÑÐ½Ð¾Ðµ Ð¾ÑÐºÐ»Ð¾Ð½ÐµÐ½Ð¸Ðµ Ð¿Ð°ÑÐ°Ð¼ÐµÑÑÐ° Ð¥Ð°Ð±Ð±Ð»Ð° Ð½ÐµÐ·Ð½Ð°ÑÐ¸ÑÐµÐ»ÑÐ½Ð¾ Ð½Ð° Ð²ÑÐµÑ ÑÑÐ°Ð´Ð¸ÑÑ ÑÐ²Ð¾Ð»ÑÑÐ¸Ð¸ ÐÑÐµÐ»ÐµÐ½Ð½Ð¾Ð¹ Ð¸ Ð´Ð°ÐµÑ $\delta H(z) \sim 10^{-5}$ Ð¿ÑÐ¸ $z = 0$, ÑÑÐ¾ Ð½Ðµ ÑÐ¿Ð¾ÑÐ¾Ð±Ð½Ð¾ ÑÐ°Ð·ÑÐµÑÐ¸ÑÑ Ð¿ÑÐ¾Ð±Ð»ÐµÐ¼Ñ &lt;&lt;$H_0$-tension&gt;&gt;. ÐÐµÐ¾Ð±ÑÐ¾Ð´Ð¸Ð¼Ð¾ Ð´Ð°Ð»ÑÐ½ÐµÐ¹ÑÐµÐµ ÑÐ°Ð·Ð²Ð¸ÑÐ¸Ðµ Ð½ÐµÐ¹ÑÑÐ¸Ð½Ð½Ð¾Ð¹ Ð°ÑÑÑÐ¾Ð½Ð¾Ð¼Ð¸Ð¸ Ð½Ð¸Ð·ÐºÐ¸Ñ ÑÐ½ÐµÑÐ³Ð¸Ð¹ Ð´Ð»Ñ ÑÐ°ÑÐ¿Ð¾Ð·Ð½Ð°Ð²Ð°Ð½Ð¸Ñ Ð¿ÑÐµÐ´ÑÐºÐ°Ð·Ð°Ð½Ð½ÑÑ Ð² ÑÐ°Ð±Ð¾ÑÐµ Ð¿Ð¾ÑÐ¾ÐºÐ¾Ð² Ð½ÐµÐ¹ÑÑÐ¸Ð½Ð¾, ÐºÐ¾ÑÐ¾ÑÑÐµ, ÑÐ¾Ð³Ð»Ð°ÑÐ½Ð¾ Ð¿Ð¾Ð»ÑÑÐµÐ½Ð½ÑÐ¼ ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÐ°Ð¼, ÑÐ²Ð»ÑÑÑÑÑ ÑÐ°Ð±Ð¾ÑÐ¸Ð¼ Ð¸Ð½ÑÑÑÑÐ¼ÐµÐ½ÑÐ¾Ð¼ Ð´Ð»Ñ Ð¿Ð¾Ð¸ÑÐºÐ° ÐÐ§Ð Ð¸ ÑÑÐ¾ÑÐ½ÐµÐ½Ð¸Ñ Ð¸Ð½ÑÐ¾ÑÐ¼Ð°ÑÐ¸Ð¸ Ð¾ ÑÐ°Ð½Ð½ÐµÐ¹ ÐÑÐµÐ»ÐµÐ½Ð½Ð¾Ð¹.
description: This work is devoted to the study of the energy spectra of neutrinos produced as a result of the evaporation of primordial black holes (PBHs), uniformly distributed throughout the Universe with a log-normal mass function. The goal of the work is to determine such parameters $\sigma, M_{\mathrm{c}}$ of the mass spectrum at which the total neutrino fluxes will be large enough so that they can be unambiguously identified, indirectly confirming the existence of PBHs; estimate the influence of the energy contribution of neutrinos from PBHs on the expansion rate of the Universe. Â  Â  The research method includes numerical calculation and analysis of differential fluxes of all types of neutrinos, taking into account the cosmological redshift $z$ and strict constraints on the prevalence of PBHs for various parameters, searching for maximum energy fluxes and taking into account the influence of their energy density on the Hubble parameter $H(z )$ for different $z$. The results show that the most favorable parameters for detecting neutrinos from PBHs are in the narrow low-energy range $10^{-8} - 10^{-5}$~MeV with median masses $10^{8}\:\text{g} \lesssim M_{\mathrm{c}} \lesssim 10^{11}$ g and width $0 \lesssim \sigma \lesssim 3.0$. The maximum energy contribution is made by neutrinos from the PBH distribution with $M_{\mathrm{c}} = 2.4 \times 10^{9}$ g and $\sigma \approx 2.8$, at which the relative deviation of the Hubble parameter is insignificant at all stages of the evolution of the Universe and gives $\delta H(z) \sim 10^{-5}$ for $z = 0$, which cannot solve the $H_0$-tension problem. Further development of low-energy neutrino astronomy is necessary to recognize the neutrino fluxes predicted in this work, which, according to the results obtained, are a working tool for searching for PBHs and clarifying information about the early Universe.