New test on general relativity and $f(T)$ torsional gravity from
  galaxy-galaxy weak lensing surveys
  We use galaxy-galaxy weak lensing data to perform a novel test on general
relativity (GR) and $f(T)$ torsional gravity. 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. 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 ${\rm{log_{10}}}\Omega_\alpha\le
-18.52_{-0.42}^{+0.80}$(stat)$_{-0.37}^{+1.50}$(sys)$ [R_c/0.015R_{200}]$ with
systematics mainly arising from the modelling of astrophysics, upon a
reasonable choice of cut-off radius for $f(T)$ gravity in form of $T + \alpha
T^2$. To our knowledge, this is the first time that GR is verified at such an
accuracy at the corresponding scales.
