Test of parametrized post-Newtonian gravity with galaxy-scale strong lensing systems

Abstract

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 $\gamma =0.995_{-0.047}^{+0.037}$ 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: $\gamma =1.000_{-0.0025}^{+0.0023}$. 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.

7 pages, 8 figures, accepted for publication in ApJ