Light deflection angle through velocity profile of galaxies in $f(R)$ model

TL;DR

This paper investigates how $f(R)$ gravity models can explain galactic rotation curves and gravitational lensing without dark matter, by analyzing light deflection angles in specific galaxy profiles and comparing with observational data.

Contribution

It introduces a novel approach to galactic dynamics using $f(R)$ gravity, deriving light deflection angles from an effective potential and testing against real galaxy data.

Findings

Light deflection angles in $f(R)$ models are consistent with observations.

The $f(R)$ model parameter $ ext{delta} extasciitilde 10^{-6}$ fits galaxy lensing data.

$f(R)$ gravity can replicate effects usually attributed to dark matter in galaxies.

Abstract

We explore a new realisation of the galactic scale dynamics via gravitational lensing phenomenon in power-law $f(R)$ gravity theory of the type $f(R)\propto R^{1+\delta}$ with $\delta<<1$ for interpreting the clustered dark matter effects. We utilize the single effective point like potential (Newtonian potential + $f(R)$ background potential) obtained under the weak field limit to study the combined observations of galaxy rotation curve beyond the optical disk size and their lensing profile in $f(R)$ frame work. We calculate the magnitude of light deflection angle with the characteristic length scale (because of Noether symmetry in $f(R)$ theories) appearing in the effective $f(R)$ rotational velocity profile of a typical galaxy with the model parameter $\delta \approx O(10^{-6})$ constrained in previous work. For instance, we work with the two nearby controversial galaxies NGC 5533 and NGC 4138 and explore their galactic features by analysing the lensing angle profiles in $f(R)$ background. We also contrast the magnitudes of $f(R)$ lensing angle profiles and the relevant parameters of such galaxies with the generalised pseudo-isothermal galaxy halo model and find consistency.