Improved constraints on the primordial power spectrum at small scales from ultracompact minihalos

Abstract

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.

7 figures, 14 pages + appendices. v2 matches version accepted for publication in PRD; updated to WMAP normalisation, updated reionisation limits, various other small changes. v3 slightly corrects the normalisation used for displaying past data in Fig 6, as well as a sign typo picked up in proof in Eq 26. All results and conclusions completely unchanged

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