Testing $f(R)$ Gravity from Cosmic Shear Measurements

Abstract

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.

Figures (4)

• Figure 1: Validation of the emulator performance by comparison with ReACT at redshift $z=1$. Four samples with $\log_{10}|f_{R_0}| = -4, -5, -6, -7$ are selected. The relative errors remain within 5%.
• Figure 2: Comparison of cosmic shear constraints on $A_\mathrm{s}$ versus $\Omega_\mathrm{m}$ (left) and $A_\mathrm{s}$ versus $\log_{10}|f_{R_0}|$ (right) from five datasets: DES-Y3, DES-Y3 Blue, KiDS-1000, HSC-Y3, and a combined DES-Y3 + KiDS-1000 analysis, with constraints derived from external datasets shown in red.
• Figure 3: Constraints on $\log_{10}|f_{R_0}|$ from the combination of cosmic shear and external datasets. The left panel depicts $\log_{10}|f_{R_0}|$ versus $A_\mathrm{s}$ and the right panel shows the relationship between $\log_{10}|f_{R_0}|$ and $\sigma_8$, where the inclusion of cosmic shear enhances the precision of the constraints, with the tightest limit obtained from the joint analysis of DES-Y3 + KiDS-1000 + All Ext.
• Figure 4: The constraints on $\log_{10}|f_{R_0}|$ from this work are compared with those from previous works. The best result from this work is shown in red, while other constraints using cosmic shear are presented in blue. Results from previous studies are depicted in black.