New test on General Relativity using galaxy-galaxy lensing with astronomical surveys

We use data from galaxy-galaxy weak lensing to perform a novel test on General Relativity (GR). In particular, we impose strong constraints using the torsional (teleparallel) formulation of gravity in which the deviation from GR is quantified by a single parameter $\alpha$, an approximation which is always valid at low-redshift Universe and weak gravitational fields. We calculate the difference in the deflection angle and eventually derive the modified Excess Surface Density profile, which is mainly affected at small scales. Hence, confronting the predictions with weak lensing data from the Sloan Digital Sky Survey (SDSS) Data Release (DR) 7 we obtain the upper bound on the deviation parameter, which, expressed via the dimensional percentage in the universe energy content, reads as $\log_{10}{\Omega_\alpha^0} \le -18.16 \pm 0.63$. To our knowledge, this is the first time that GR is verified at such an accuracy at the corresponding scales.