Galactic dynamics in the presence of scalaron: A perspective from $\boldsymbol{f(R)}$ gravity

Abstract: We consider $f(R)$ modified gravity theory incorporating the chameleon mechanism to address galactic dynamics. By employing the metric formalism and utilizing a conformal transformation, we simplify the field equations and describe the extra degree of freedom $f_{R}$ via a scalar field (scalaron) with chameleonic behavior. A recently proposed $f(R)$ model is analyzed to illustrate this behavior effectively. Subsequently, the rotational velocity equation including the scalaron's contribution is derived for a test particle in a static, spherically symmetric spacetime. Then we generate rotation curves and fit them to observational data of thirty seven galaxies using two fitting parameters, $M_0$ and $r_c$, the total mass and core radius of a galaxy respectively.