2024ApJ...969..119W

We use galaxy-galaxy lensing data to test general relativity and f(T) gravity at galaxy scales. We consider an exact spherically symmetric solution of f(T) theory, which is obtained from an approximate quadratic correction, and thus it is expected to hold for every realistic deviation from general relativity. Quantifying the deviation by a single parameter Q, and following the post-Newtonian approximation, we obtain the corresponding deviation in the gravitational potential, shear component, and effective excess surface density profile. We used five stellar mass samples and divided them into blue and red galaxies to test the model dependence on galaxy color, and we modeled the excess surface density profiles using the Navarro-Frenk-White profiles. Based on the group catalog from the Sloan Digital Sky Survey Data Release 7 (SDSS DR7) we finally extract $Q=-{2.138}_{-0.516}^{+0.952}\times {10}^{-5}\,$ Mpc^–2 at 1σ confidence. This result indicates that f(T) corrections on top of general relativity are favored. Finally, we apply information criteria, such as the Akaike and Bayesian ones, and although the dependence of f(T) gravity on the off-center effect implies that its optimality needs to be carefully studied, our analysis shows that f(T) gravity is more efficient in fitting the data compared to general relativity and the ΛCDM paradigm, and thus it offers a challenge to the latter.