Tau neutrinos from ultracompact dark matter minihalos and constraints on
  the primordial curvature perturbations
  The observations and research on the neutrinos provide a kind of indirect way
of revealing the properties of dark matter particles. For the detection of muon
neutrinos, the main issue is the large atmospheric background, which is caused
by the interactions between the cosmic rays and atoms within the atmosphere.
Compared with muon neutrinos, tau neutrinos have a smaller atmospheric
background especially for the downward-going direction. Except for the
classical neutrino sources, dark matter particles can also annihilate into the
neutrinos and are the potential high energy astrophysical sources. The
annihilation rate of dark matter particles is proportional to the square of
number density; therefore, the annihilation rate is large near the center of
dark matter halos especially for the new kind of dark matter structures named
ultracompact dark matter minihalos (UCMHs). In previous works, we have
investigated the potential muon neutrino flux from UCMHs due to dark matter
annihilation. Moreover, since the formation of UCMHs is related to the
primordial density perturbations of small scales, we get the constraints on the
amplitude of the primordial curvature perturbations of small scales, $1
\lesssim k \lesssim 10^{7} ~\rm Mpc^{-1}$. In this work, we focus on the
downward-going tau neutrinos from UCMHs due to dark matter annihilation.
Compared with the background of tau neutrino flux we get the constraints on the
mass fraction of UCMHs. Then using the limits on the mass fraction of UCMHs we
got the constraints on the amplitude of the primordial curvature perturbations
which are extended to the scale $k \sim 10^{8} ~ \rm Mpc^{-1}$ compared with
previous results.
