Strong gravitational lensing in $f\left(\chi\right)=\chi^{3/2}$ gravity

Understand

We discuss the phenomenology of gravitational lensing in the purely metric $f\left(\chi\right)$ gravity, an $f(R)$ gravity where the action of the gravitational field depends on the source mass.

• We focus on the strong lensing regime in galaxy-galaxy lens systems and in clusters of galaxies.
• Using an approximate metric solution accurate to second order of the velocity field $v/c$, we show how, in the $f\left(\chi\right)=\chi^{3/2}$ gravity, the same light deflection can be produced by point-like lenses with masses smaller than in General Relativity; this mass difference increases with increasing impact parameter and decreasing lens mass.
• However, for sufficiently massive point-like lenses and small impact parameters, $f\left(\chi\right)=\chi^{3/2}$ and GR yield indistinguishable light deflection angles: this regime occurs both in observed galaxy-galaxy lens systems and in the central regions of galaxy clusters.