Testing $f(R)$ Gravity from Cosmic Shear Measurements
In this work, we perform a detailed analysis to constrain the Hu-Sawicki \(f(R)\) gravity model, using cosmic shear data from three prominent Stage-III weak lensing surveys: DES-Y3, KiDS-1000, and HSC-Y3. To accurately model the nonlinear matter clustering in the analysis of cosmic shear signals, we employ \texttt{FREmu}, a recently developed power spectrum emulator for the \(f(R)\) gravity trained on the Quijote-MG simulations. This emulator achieves precise predictions, limiting the errors to 5\% on scales of \(0.009h\,{\rm Mpc}^{-1} < k < 0.5h\,{\rm Mpc}^{-1}\). Our findings reveal that cosmic shear data alone impose only weak constraints on the \(f(R)\) parameter \(\log_{10}|f_{R_0}|\). To improve these constraints, we incorporate state-of-the-art external observations, including data from the cosmic microwave background and baryon acoustic oscillations. The inclusion of these external datasets significantly enhances the constraints, yielding an upper limit of \(\log_{10}|f_{R_0}| < -4.98\) at the 95\% confidence level.