Galactic dynamics in the presence of scalaron: A perspective from f(R) gravity

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 fR 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, M₀ and rc, the total mass and core radius of a galaxy respectively.