Cosmological boost factor for dark matter annihilation at redshifts of $z=10$-$100$ using the power spectrum approach

Abstract

We compute the cosmological boost factor at high redshifts of $z=10$-$100$ by integrating the non-linear matter power spectrum measured from high-resolution cosmological $N$-body simulations. An accurate boost factor is required to estimate the energy injection from dark matter annihilation, which may affect the cosmological re-ionization process. We combined various box-size simulations (side lengths of $1\mathrm{kpc}$-$10\mathrm{Mpc}$) to cover a wide range of scales, i.e. $k=1$-$10^7{\mathrm{Mpc}}^{-1}$. The boost factor is consistent with the linear theory prediction at $z\gtrsim 50$ but strongly enhanced at $z\lesssim 40$ as a result of non-linear matter clustering. Although dark matter free-streaming damping was imposed at $k_{\mathrm{fs}}=10^6{\mathrm{Mpc}}^{-1}$ in the initial power spectrum, the damping disappears at later times of $z\lesssim 40$ as a result of the power transfer from large to small scales. Because the simulations do not explore very small-scale clustering at $k>10^7{\mathrm{Mpc}}^{-1}$, our result is a lower bound on the boost factor at $z\lesssim 40$. A simple fitting function of the boost factor is also presented.

12 pages, 5 figures, accepted for publication in PRD