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 nonlinear 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 reionization process. We combined various box-size simulations (side lengths of 1 kpc-10 Mpc) to cover a wide range of scales, i.e., k =1 - 10⁷ Mpc^-1 . The boost factor is consistent with the linear theory prediction at z ≳50 but strongly enhanced at z ≲40 as a result of nonlinear matter clustering. Although dark matter free-streaming damping was imposed at k_fs=10⁶ Mpc^-1 in the initial power spectrum, the damping disappears at later times of z ≲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 >10⁷ Mpc^-1, our result is a lower bound on the boost factor at z ≲40 . A simple fitting function of the boost factor is also presented.