Test of Parameterized 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 γ ={0.995}_-0.047^+0.037 under the assumption of a flat ΛCDM universe with parameters taken from Planck observations. General relativity (GR) predicts exactly γ = 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 ∼25%. By applying a cosmological model-independent method to the simulated future LSST data, we found a significant degeneracy between the PPN γ parameter and the spatial curvature of the universe. Setting a prior on the cosmic curvature parameter -0.007 < Ω_k < 0.006, we obtained the constraint on the PPN parameter that γ ={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 future lens surveys.