Testing <i>f</i>(<i>R</i>) 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: Dark Energy Survey Year 3, KiDS-1000, and Hyper Suprime-Cam Year 3. To accurately model the nonlinear matter clustering in the analysis of cosmic shear signals, we employ 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 0.009 h Mpc −1 &lt; k &lt; 0.5 h Mpc −1 . Our findings reveal that cosmic shear data alone impose only weak constraints on the f ( R ) parameter <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>log</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>10</mml:mn> </mml:mrow> </mml:msub> <mml:mo stretchy="false">∣</mml:mo> <mml:msub> <mml:mrow> <mml:mi>f</mml:mi> </mml:mrow> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>R</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>0</mml:mn> </mml:mrow> </mml:msub> </mml:mrow> </mml:msub> <mml:mo stretchy="false">∣</mml:mo> </mml:math> . 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 data sets significantly enhances the constraints, yielding an upper limit of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>log</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>10</mml:mn> </mml:mrow> </mml:msub> <mml:mo stretchy="false">∣</mml:mo> <mml:msub> <mml:mrow> <mml:mi>f</mml:mi> </mml:mrow> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>R</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>0</mml:mn> </mml:mrow> </mml:msub> </mml:mrow> </mml:msub> <mml:mo stretchy="false">∣</mml:mo> <mml:mo>&lt;</mml:mo> <mml:mo>−</mml:mo> <mml:mn>4.98</mml:mn> </mml:math> at the 95% confidence level.