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Ultracompact minihalos would be formed if there are larger densityperturbations ($0.0003 < \delta\rho/\rho < 0.3$) in the earlier epoch. Thedensity profile of them is steeper than the standard dark matter halos. If thedark matter can annihilate or decay into the standard particles, e.g., photons,these objects would be the potential astrophysical sources. In order to beconsistent with the observations, such as $Fermi$, the abundance ofultracompact minihalos must be constrained. On the other hand, the formation ofthese objects has very tight relation with the primordial curvatureperturbations on smaller scale, so the fraction of ultracompact minihalos isvery important for modern cosmology. In previous works, the studies are focusedon the dark matter annihilation for these objects. But if the dark matter isnot annihilated, the dark matter decay is another important possible case. Onthe other hand, the abundance of ultracompact minihalos is related to manyother parameters, such as the mass of dark matter, the decay channels and thedensity profile of dark matter halo. One of the important aspects of this workis that we investigate the $\gamma$-ray signals from nearby ultracompactminihalos due to dark matter decay and another important aspect is to study indetail how the different decay channels and density profiles affect theconstraints on the abundance of ultracompact minihalos.

Dark Matter Decay and the Abundance of Ultracompact Minihalos