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 $\mathtt{\text{FREmu}}$, 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 $0.009h{\mathrm{M}\mathrm{p}\mathrm{c}}^{-1}<k<0.5h{\mathrm{M}\mathrm{p}\mathrm{c}}^{-1}$. Our findings reveal that cosmic shear data alone impose only weak constraints on the $f(R)$ parameter ${\log }_{10}\mathrm{\mid }{f}_{R_0}\mathrm{\mid }$. 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 ${\log }_{10}\mathrm{\mid }{f}_{R_0}\mathrm{\mid }<-4.98$ at the 95% confidence level.