SIMBAD references

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 presumption of a specific cosmological model based on GR, we employ the distance sum rule in the Friedmann-Lemaitre-Robertson-Walker metric to directly estimate the parameterized post-Newtonian (PPN) parameter γ _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 _PPN and Ω_ k _ without any assumptions about the contents of the universe or the theory of gravity. Our results show that γ_PPN={1.11}{-0.09}^{+0.11} and {Ω}_{k}={0.48}{-0.71}^{+1.09}, indicating a strong degeneracy between the two quantities. The measured γ _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_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 _PPN = 1), our results are still marginally compatible with zero curvature ({Ω}_{{k}=–{0.12}}{-0.36}^{+0.48}), supporting no significant deviation from a flat universe.