Neutrino bound states and bound systems

Yukawa interactions of neutrinos with a new light scalar boson $\phi$ can lead to formation stable bound states and systems many ($\nu$-clusters). For allowed values the coupling $y$ mass $m_\phi$, state two would have size larger than $10^{12}$ cm. Bound sub-cm sizes are possible for keV scale sterile $y > 10^{-4}$. $\nu$-clusters we study in detail properties final configurations. If there is an efficient cooling mechanism, these configurations degenerate Fermi gas. We formulate solve equations density distributions $\nu$-clusters. In non-relativistic case, they reduced Lane-Emden equation. find that (i) exist any number neutrinos, $N$; (ii) maximal central $\sim 10^9$ cm$^{-3}$ determined by neutrino mass; (iii) given $m_\phi$ minimal value $Ny^3$ which be formed; (iv) strength interaction, $S_\phi = (ym_\nu/m_\phi)^2$, radius exists. discuss from relic background process expansion Universe. One possibility realized 700$ development instabilities $\nu$-background at $T < m_\nu$ leads its fragmentation. $y$, due $\phi$-bremsstrahlung annihilation negligible. The may range $\sim$ km 5$ Mpc. Formation clusters affects perspectives detection neutrinos.