The Potential Role of Modified Gravity in Explaining Galactic Rotation Curves

Abstract: The discrepancy between observed galactic rotation curves and predictions from Newtonian dynamics has been traditionally explained by the presence of dark matter halos. However, an alternative approach suggests that modifications to gravity at galactic and cosmological scales could account for these deviations without invoking unseen mass. This paper explores how modified gravity models, including MOND (Modified Newtonian Dynamics), f(R) gravity, scalar-tensor theories, and emergent gravity, may provide a theoretical explanation for the observed rotational behavior of galaxies. We analyze these alternative gravity models using dynamical stability conditions, empirical galaxy rotation data, and numerical simulations, comparing their predictions with those of standard ΛCDM cosmology. Additionally, we explore whether gravitational wave constraints, strong lensing observations, and large-scale structure surveys can distinguish between modified gravity effects and the presence of dark matter. Key Highlights: Comparison of modified gravity models with dark matter-based explanations for rotation curves. Analytical derivation of modified field equations applied to galactic dynamics. Observational constraints from galaxy rotation curves, weak lensing, and large-scale surveys. Implications for alternative gravity theories, including MOND, f(R), and scalar-tensor gravity. Predictions for upcoming astrophysical observations to distinguish between competing models. By combining theoretical modeling, observational data, and computational simulations, this paper presents a comprehensive evaluation of whether modified gravity theories can provide a viable alternative to dark matter in explaining galactic rotation curves. Keywords: Modified gravity, MOND, f(R) gravity, galactic rotation curves, dark matter alternatives, alternative gravity theories, weak lensing, scalar-tensor gravity, emergent gravity, astrophysics.