Constraint on the post-Newtonian parameter $\gamma$ on galactic size scales

We constrain the post-Newtonian gravity parameter $\gamma$ on kiloparsec scales by comparing the masses of 15 elliptical lensing galaxies from the Sloan Lens ACS Survey as determined in two independent ways. The first method assumes only that Newtonian gravity is correct and is independent of $\gamma$, while the second uses gravitational lensing which depends on $\gamma$. More specifically, we combine Einstein radii and radial surface-brightness gradient measurements of the lens galaxies with empirical distributions for the mass concentration and velocity anisotropy of elliptical galaxies in the local universe to predict $\gamma$-dependent probability distributions for the lens-galaxy velocity dispersions. By comparing with observed velocity dispersions, we derive a maximum-likelihood value of $\gamma =0.98\pm 0.07$ (68% confidence). This result is in excellent agreement with the prediction of general relativity that $\gamma =1$, which has previously been verified to this accuracy only on solar-system length scales.

Figure 1

Normalized likelihood densities for the post-Newtonian parameter $\gamma$ derived from individual SLACS GLGs ( gray), with joint likelihood for the entire sample (black). The joint distribution is approximately Gaussian, giving $\gamma =0.98\pm 0.07$ (68% confidence).