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 non-linear matter power spectrum measured from high-resolution $N$-body simulations. An accurate is required to estimate energy injection dark annihilation, which may affect re-ionization process. combined various box-size simulations (side lengths $1 \, {\rm kpc}$-$10 Mpc}$) cover a wide range scales, i.e. $k=1$-$10^7 Mpc}^{-1}$. The consistent with linear theory prediction $z \gtrsim 50$ but strongly enhanced \lesssim 40$ as result clustering. Although free-streaming damping was imposed $k_{\rm fs}=10^6 Mpc}^{-1}$ in initial spectrum, disappears later times $z\lesssim40$ transfer large small scales. Because do not explore very small-scale clustering $k>10^7 Mpc}^{-1}$, our lower bound on 40$. A simple fitting function also presented.