  For a Gaussian spectrum of primordial density fluctuations, ultracompact
minihalos (UCMHs) of dark matter are expected to be produced in much greater
abundance than, e.g., primordial black holes. Forming shortly after
matter-radiation equality, these objects would develop very dense and spiky
dark matter profiles. In the standard scenario where dark matter consists of
thermally-produced, weakly-interacting massive particles, UCMHs could thus
appear as highly luminous gamma-ray sources, or leave an imprint in the cosmic
microwave background by changing the reionisation history of the Universe. We
derive corresponding limits on the cosmic abundance of UCMHs at different
epochs, and translate them into constraints on the primordial power spectrum.
We find the resulting constraints to be quite severe, especially at length
scales much smaller than what can be directly probed by the cosmic microwave
background or large-scale structure observations. We use our results to provide
an updated compilation of the best available constraints on the power of
density fluctuations on all scales, ranging from the present-day horizon to
scales more than 20 orders of magnitude smaller.
