Gravity lens critical test for gravity constants and dark sector

The recent study of the strong gravitational lens ESO 325-G004 (Collett et al., Science, 360:1342, 2018) leads to a new possibility for testing General Relativity and its extensions. Such gravity lens observational studies can be instrumental for establishing a limitation on the precision of testing General Relativity in the weak-field regime and on the two gravity constants (the Newtonian and cosmological ones) as described in Gurzadyan and Stepanian (Eur Phys J C 78:632 2018). Namely, we predict a critical value for the involved weak-field parameter \(\gamma _{cr}=0.998\) (for \(M=1.5\,\,10^{11}\, M_{\odot }\) lens mass and \(r=2\, kpc\) light impact distance), which remarkably does not depend on any hypothetical variable but is determined only by well measured quantities. If the critical parameter \(\gamma _{cr}\) will be established at future observations, this will mark the first discrepancy with General Relativity of the conventional weak-field Newtonian limit, directly linked to the nature of the dark sector of the Universe.