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

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 $1 \, {\rm kpc}$-$10 \, {\rm Mpc}$) to cover a wide range of scales, i.e. $k=1$-$10^7 \, {\rm Mpc}^{-1}$. 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 $k_{\rm fs}=10^6 \, {\rm Mpc}^{-1}$ in the initial power spectrum, the damping disappears at later times of $z\lesssim40$ as a result of the power transfer from large to small scales. Because the simulations do not explore very small-scale clustering at $k>10^7 \, {\rm Mpc}^{-1}$, 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.