Revisiting Dark Matter Theories through Modified Newtonian and Relativistic Frameworks

Abstract: The nature of dark matter remains one of the greatest unsolved problems in modern physics. While the standard ΛCDM model successfully explains large-scale cosmic structures, persistent anomalies in galactic rotation curves, gravitational lensing profiles, and cosmic microwave background (CMB) data suggest the need for alternative approaches. This paper revisits dark matter theories through the lens of Modified Newtonian Dynamics (MOND) and relativistic extensions, assessing whether these frameworks can provide a viable alternative to particle-based dark matter models. We explore how MONDian gravity, f(R) gravity, and other modified relativistic theories affect galactic dynamics, large-scale structure formation, and gravitational lensing. Using analytical models, numerical simulations, and observational constraints from high-precision astrophysical surveys, we evaluate whether modified gravity frameworks can resolve dark matter-related discrepancies in a way consistent with observed cosmic phenomena. Key Highlights: Comparative analysis of MOND, f(R) gravity, and relativistic extensions as alternatives to dark matter. Impact on galactic rotation curves, cluster dynamics, and cosmic expansion. Constraints from gravitational lensing, CMB anisotropies, and cosmological structure formation. Potential deviations from General Relativity (GR) and their observational signatures. Testing predictions with upcoming astronomical surveys and gravitational wave experiments. By integrating insights from modified gravity and dark matter research, this work provides a comprehensive reassessment of alternative explanations for missing mass, offering a pathway toward new physics beyond the Standard Model and General Relativity. Keywords: Dark matter, Modified Newtonian Dynamics, MOND, f(R) gravity, gravitational lensing, galactic rotation curves, modified gravity, relativistic frameworks, cosmology, large-scale structure formation.