Test of parametrized post-Newtonian gravity with galaxy-scale strong
  lensing systems
  Based on a mass-selected sample of galaxy-scale strong gravitational lenses
from the SLACS, BELLS, LSD and SL2S surveys and using a well-motivated fiducial
set of lens-galaxy parameters we tested the weak-field metric on kiloparsec
scales and found a constraint on the post-Newtonian parameter $\gamma =
0.995^{+0.037}_{-0.047}$ under the assumption of a flat $\Lambda$CDM universe
with parameters taken from \textit{Planck} observations. General relativity
(GR) predicts exactly $\gamma=1$. Uncertainties concerning the total mass
density profile, anisotropy of the velocity dispersion and the shape of the
light-profile combine to systematic uncertainties of $\sim 25\%$. By applying a
cosmological model independent method to the simulated future LSST data, we
found a significant degeneracy between the PPN $\gamma$ parameter and spatial
curvature of the Universe. Setting a prior on the cosmic curvature parameter
$-0.007< \Omega_k <0.006$, we obtained the following constraint on the PPN
parameter: $\gamma=1.000^{+0.0023}_{-0.0025}$. We conclude that strong-lensing
systems with measured stellar velocity dispersions may serve as another
important probe to investigate validity of the GR, if the mass-dynamical
structure of the lensing galaxies is accurately constrained in the future lens
surveys.
