Paper detail

Direct Estimate of the Post-Newtonian Parameter and Cosmic Curvature from Galaxy-scale Strong Gravitational Lensing

Einstein's theory of general relativity (GR) has been precisely tested on solar system scales, but extragalactic tests are still poorly performed. In this work, we use a newly compiled sample of galaxy-scale strong gravitational lenses to test the validity of GR on kiloparsec scales. In order to solve the circularity problem caused by the preassumption of a specific cosmological model based on GR, we employ the distance sum rule in the Friedmann-Lema\^ıtre-Robertson-Walker metric to directly estimate the parameterized post-Newtonian (PPN) parameter $γ_{\rm PPN}$ and the cosmic curvature $Ω_k$ by combining observations of strong lensing and Type Ia supernovae. This is the first simultaneous measurement of $γ_{\rm PPN}$ and $Ω_k$ without any assumptions about the contents of the universe or the theory of gravity. Our results show that $γ_{\rm PPN}=1.11^{+0.11}_{-0.09}$ and $Ω_{k}=0.48^{+1.09}_{-0.71}$, indicating a strong degeneracy between the two quantities. The measured $γ_{\rm PPN}$, which is consistent with the prediction of 1 from GR, provides a precise extragalactic test of GR with a fractional accuracy better than 9.0\%. If a prior of the spatial flatness (i.e., $Ω_{k}=0$) is adopted, the PPN parameter constraint can be further improved to $γ_{\rm PPN}=1.07^{+0.07}_{-0.07}$, representing a precision of 6.5\%. On the other hand, in the framework of GR (i.e., $γ_{\rm PPN}=1$), our results are still marginally compatible with zero curvature ($Ω_k=-0.12^{+0.48}_{-0.36}$), supporting no significant deviation from a flat universe.