Exploring Modified Gravity Models and Their Impact on Cosmic Expansion

Abstract: The accelerated expansion of the universe, traditionally attributed to dark energy, has led to the exploration of modified gravity models as alternative explanations. This paper investigates how deviations from Einstein’s General Relativity (GR)—such as f(R) gravity, scalar-tensor theories, massive gravity, and extra-dimensional models—could provide a theoretical basis for cosmic acceleration without invoking an unknown dark energy component. Using cosmological perturbation theory, large-scale structure formation data, and gravitational wave constraints, we analyze how these modified gravity frameworks affect the Hubble parameter evolution, cosmic microwave background anisotropies, and the dynamics of large-scale structures. We also explore how current and future astronomical surveys (Euclid, LSST, JWST) can test predictions of these models against the ΛCDM paradigm. Key Highlights: Comparative analysis of f(R), scalar-tensor, and extra-dimensional gravity models. Impacts on cosmic expansion, galaxy clustering, and large-scale structure formation. Potential deviations from general relativity in gravitational wave propagation. Observational constraints from Type Ia supernovae, cosmic microwave background, and baryon acoustic oscillations. Future testability through next-generation astronomical surveys. By linking theoretical extensions of gravity with observational data, this work provides a framework for assessing whether modified gravity models can resolve the cosmic acceleration problem while remaining consistent with astrophysical and cosmological constraints. Keywords: Modified gravity, cosmic expansion, f(R) gravity, scalar-tensor theory, dark energy alternatives, general relativity extensions, large-scale structure, cosmological perturbations, gravitational waves, observational cosmology.