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