Accurate predictions for the nonlinear matter power spectrum are needed to confront theory with observations in current and near future weak-lensing and galaxy clustering surveys. We propose a computationally cheap method to create an emulator for modified gravity models by utilizing existing emulators for $\mathrm{\Lambda }\mathrm{CDM}$. Using a suite of $N$-body simulations, we construct a fitting function for the enhancement of both the linear and nonlinear matter power spectrum in the commonly studied Hu-Sawicki $f(R)$ gravity model valid for wave numbers $k\lesssim 5–10h{\mathrm{Mpc}}^{-1}$ and redshifts $z\lesssim 3$. We show that the cosmology dependence of this enhancement is relatively weak so that our fit, using simulations coming from only one cosmology, can be used to get accurate predictions for other cosmological parameters. We also show that the cosmology dependence can, if needed, be included by using linear theory, approximate $N$-body simulations (such as comoving lagrangian acceleration) and semianalytical tools like the halo model. Our final fit can easily be combined with any emulator or semianalytical models for the nonlinear $\mathrm{\Lambda }\mathrm{CDM}$ power spectrum to accurately, and quickly, produce a nonlinear power spectrum for this particular modified gravity model. The method we use can be applied to fairly cheaply construct an emulator for other modified gravity models. As an application of our fitting formula, we use it to compute Fisher forecasts for how well galaxy clustering and weak lensing in a Euclid-like survey will be at constraining modifications of gravity.

• Received 9 May 2019

DOI:https://doi.org/10.1103/PhysRevD.100.123540