Modeling the nonlinear clustering in modified gravity models. I. a fitting formula for matter power spectrum of ƒ (R) gravity

Based on a suite of N-body simulations of the Hu-Sawicki model of ƒ(R) gravity with different sets of model and cosmological parameters, we develop a new fitting formula with a numeric code, MGHalofit, to calculate the nonlinear matter power spectrum P(k) for the Hu-Sawicki model. We compare the MGHalofit predictions at various redshifts (z ≤ 1) to the f(R) simulations and find that the relative error of the MGHalofit fitting formula of P(k) is no larger than 6% at k ≤ 1 h Mpc^–1 and 12% at k (1, 10] h Mpc^–1, respectively. Based on a sensitivity study of an ongoing and a future spectroscopic survey, we estimate the detectability of a signal of modified gravity described by the Hu-Sawicki model using the power spectrum up to quasi-nonlinear scales.