Probing the dark matter issue in f(R)-gravity via gravitational lensing

TL;DR

This paper examines f(R)-gravity theories in the weak field limit, showing that gravitational lensing predictions are identical to General Relativity, implying dark matter cannot be replaced by these theories based on lensing data.

Contribution

It demonstrates that f(R)-gravity theories do not alter gravitational lensing predictions in the post-Newtonian limit, challenging their ability to eliminate dark matter from lensing observations.

Findings

Lensing observables in f(R)-gravity match those of General Relativity.

Dark matter remains necessary for explaining lensing phenomena.

f(R)-gravity cannot be constrained by lensing in the post-Newtonian regime.

Abstract

For a general class of analytic f(R)-gravity theories, we discuss the weak field limit in view of gravitational lensing. Though an additional Yukawa term in the gravitational potential modifies dynamics with respect to the standard Newtonian limit of General Relativity, the motion of massless particles results unaffected thanks to suitable cancellations in the post-Newtonian limit. Thus, all the lensing observables are equal to the ones known from General Relativity. Since f(R)-gravity is claimed, among other things, to be a possible solution to overcome for the need of dark matter in virialized systems, we discuss the impact of our results on the dynamical and gravitational lensing analyses. In this framework, dynamics could, in principle, be able to reproduce the astrophysical observations without recurring to dark matter, but in the case of gravitational lensing we find that dark matter is an unavoidable ingredient. Another important implication is that gravitational lensing, in the post-Newtonian limit, is not able to constrain these extended theories, since their predictions do not differ from General Relativity.