Gamma-rays from ultracompact minihalos: potential constraints on the
  primordial curvature perturbation
  Ultracompact minihalos (UCMHs) are dense dark matter structures which can
form from large density perturbations shortly after matter-radiation equality.
If dark matter is in the form of Weakly Interacting Massive Particles (WIMPs),
then UCMHs may be detected via their gamma-ray emission. We investigate how the
{\em{Fermi}} satellite could constrain the abundance of UCMHs and place limits
on the power spectrum of the primordial curvature perturbation. Detection by
{\em Fermi} would put a lower limit on the UCMH halo fraction. The smallest
detectable halo fraction, $f_{\rm UCMH} \gtrsim 10^{-7}$, is for $M_{\rm UCMH}
\sim 10^{3} M_{\odot}$. If gamma-ray emission from UCMHs is not detected, an
upper limit can be placed on the halo fraction. The bound is tightest, $f_{\rm
UCMH} \lesssim 10^{-5}$, for $M_{\rm UCMH} \sim 10^{5} M_{\odot}$. The
resulting upper limit on the power spectrum of the primordial curvature
perturbation in the event of non-detection is in the range $\mathcal{P_R}
\lesssim 10^{-6.5}- 10^{-6}$ on scales $k \sim 10^{1}-10^{6} \, {\rm
Mpc}^{-1}$. This is substantially tighter than the existing constraints from
primordial black hole formation on these scales, however it assumes that dark
matter is in the form of WIMPs and UCMHs are not disrupted during the formation
of the Milky Way halo.
