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 Data Release 7 we obtain the upper bound on the deviation parameter , which , expressed via the dimensionless percentage in the universe energy content , reads as { { log _ { 10 } } } \Omega _ { \alpha } \leq - 18.52 _ { -0.42 } ^ { +0.80 } ( stat . ) _ { -0.39 } ^ { +1.50 } ( sys . ) with systematics mainly arising from the modelling .
To our knowledge , this is the first time that GR is verified at such an accuracy at the corresponding scales