Gravity lens critical test for gravity constants and dark sector

Abstract: The recent study of the strong gravitational lens ESO 325-G004 [1] 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 [2]. 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 conventional weak-field Newtonian limit, directly linked to the nature of dark sector of the Universe.