Galaxy-galaxy lensing data: $f(T)$ gravity challenges General Relativity

We use galaxy-galaxy lensing data to test General Relativity and $f(T)$ gravity at galaxies 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 to test the model dependence on galaxy color, and we modeled the excess surface density (ESD) profiles using the Navarro-Frenk-White (NFW) profiles. Based on the group catalog from the Sloan Digital Sky Survey Data Release 7 (SDSS DR7) we finally extract $Q=-2.138^{+0.952}_{-0.516}\times 10^{-5}\,$Mpc$^{-2}$ at $1\sigma$ confidence. This result indicates that $f(T)$ corrections on top of General Relativity are favored. Finally, we apply information criteria, such as the AIC and BIC 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 comparing to General Relativity and $\Lambda$CDM paradigm, and thus it offers a challenge to the latter.