Neutrino signals from ultracompact minihalos and constraints on the primordial curvature perturbation

Compared with that of standard dark matter halos, the density profile of the recently proposed new kind of dark matter structure named ultracompact minihalos (UCMHs) is steeper and its formation time is earlier. If the dark matter is composed of weakly interactive massive particles, the potential signals, e.g., neutrinos, from UCMHs due to dark matter annihilation would be detected by IceCube/DeepCore or other detectors and such signals would have a very useful complementarity of $\gamma$-ray observations. On the other hand, the formation of UCMHs is related to primordial curvature perturbations on the smaller scales. So constraints on the abundance of UCMHs can be used to give a limit on the perturbations on these scales. In previous works in the literature, the authors focused on the $\gamma$-ray signals from UCMHs due to dark matter annihilation. In this work, we investigate the neutrino signals from nearby UCMHs. Although no excess of neutrino signals from dark matter annihilation has been observed, the constraints on the abundance of UCMHs can be obtained and these constraints can be translated into the limit on the primordial curvature perturbations on small scales.