Probing dark fluids and modified gravity with gravitational lensing

Abstract We generalize the Rindler-Ishak (2007) result for lensing deflection angle in a SdS spacetime, to case of general spherically symmetric fluid beyond cosmological constant. thus derive an analytic expression first post-Newtonian order static metric form $ds^2 = f(r)dt^{2} -\frac{dr^{2}}{f(r)}-r^{2}(d\theta ^2 +\sin \theta d\phi ^2)$ with $f(r) 1 - \frac{2m}{r}-\sum _{i} b_i\,\, r_0^{-q_i}\,\, \left( \frac{r_0}{r}\right)^{q_i}$ where r0 is impact parameter, $b_i\ll r_0^{q_i}$, m mass lens and qi are real arbitrary constants related properties that surrounds or modified gravity. This generalization well known Kiselev black hole metric. The approximate verified by exact numerical derivation special cases it reduces results previous studies. density pressure induces this derived terms bi. Schwarzschild perturbed dark (eg vacuum energy) studied some detail consistency Rindler Ishak found constant background. Observational data Einstein radii from distant clusters galaxies lead observational constraints on bi through them fluids, field theories gravity could induce