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Constraints on small-scale primordial density fluctuation from cosmic microwave background through dark matter annihilation

The cosmic microwave background (CMB) observation by the Planck satellite precisely determines primordial curvature fluctuations on larger scales than $\mathcal O(1)\,\mathrm{Mpc}$, while the small-scale curvature fluctuation is still less constrained. The constraint on small-scale fluctuations is highly improved if we assume the standard thermal relic dark matter scenario. When small-scale fluctuations are large enough, dense regions collapse to form small halos even in a redshift $z\gtrsim10^3$, which is called ultracompact minihalos. These minihalos enhance the annihilation of the dark matter and it is constrained by observations such as extragalactic gamma rays and the CMB. We revisit the effect of minihalos formed by the small-scale density fluctuations and calculate the ionization history modified by the dark matter annihilation. We perform the Markov Chain Monte Carlo method to constrain the size of small-scale curvature fluctuations by the CMB power spectrum. It is found that the constraint from the CMB power spectrum is comparable to that from the extragalactic gamma rays. We confirm that our constraint mainly comes from the energy injection in early time ($z\gtrsim 100$) and hence it is independent of the uncertainty of minihalo properties in the late time.