Emulators for the non-linear matter power spectrum beyond $\Lambda$CDM

Accurate predictions for the non-linear 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 $\Lambda$CDM. Using a suite of $N$-body simulations we construct a fitting function for the enhancement of both the linear and non-linear matter power spectrum in the commonly studied Hu-Sawicki $f(R)$ gravity model valid for wave-numbers $k \lesssim 5-10\, h\text{Mpc}^{-1}$ 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 COLA) and semi-analytical tools like the halo model. Our final fit can easily be combined with any emulator or semi-analytical models for the non-linear $\Lambda$CDM power spectrum to accurately, and quickly, produce a non-linear 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.