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

TL;DR

This paper explores gravitational lensing in a modified gravity theory, showing that it can mimic dark matter effects in some regimes but still requires dark matter to fully explain observed phenomena.

Contribution

It provides an approximate metric solution for $f(\chi)=\chi^{3/2}$ gravity and analyzes its implications for strong lensing, highlighting limitations in replacing dark matter.

Findings

$f(\chi)=\chi^{3/2}$ gravity can produce similar light deflection with smaller lens masses.

In galaxy-galaxy systems, masses are compatible with stellar populations without dark matter.

In galaxy cluster cores, dark matter remains necessary even in this modified gravity.

Abstract

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. In the former systems, the GR and $f\left(\chi\right)$ masses are compatible with the mass of standard stellar populations and little or no dark matter, whereas, on the scales of the core of galaxy clusters, the presence of substantial dark matter is required both in General Relativity, and in our approximate $f\left(\chi\right)=\chi^{3/2}$ point-like lens solution. We thus conclude that our approximate metric solution of $f\left(\chi\right)=\chi^{3/2}$ is unable to describe the observed phenomenology of the strong lensing regime without the aid of dark matter.