FREmu: Power Spectrum Emulator for $f(R)$ Gravity

To investigate gravity in the non-linear regime of cosmic structure using measurements from Stage-IV surveys, it is imperative to accurately compute large-scale structure observables, such as non-linear matter power spectra, for gravity models that extend beyond general relativity. However, the theoretical predictions of non-linear observables are typically derived from N-body simulations, which demand substantial computational resources. In this study, we introduce a novel public emulator, termed FREmu, designed to provide rapid and precise forecasts of non-linear power spectra specifically for the Hu-Sawicki $f(R)$ gravity model across scales $0.0089 h \mathrm{Mpc}^{-1}<k<0.5 h \mathrm{Mpc}^{-1}$ and redshifts $0<z<3$. FREmu leverages Principal Component Analysis and Artificial Neural Networks to establish a mapping from parameters to power spectra, utilizing training data derived from the Quijote-MG simulation suite. With a parameter space encompassing 7 dimensions, including $\Omega_m$, $\Omega_b$, $h$, $n_s$, $\sigma_8$, $M_{\nu}$ and $f_{R_0}$, the emulator achieves an accuracy exceeding 95% for the majority of cases, thus proving to be highly efficient for constraining parameters.