2025, Vol. 6, Issue 2, Part D
Modified gravity theories as alternatives to dark matter: A mathematical perspective
Author(s): Deep Prabha Bharti
Abstract: Modified gravity theories have emerged as compelling alternatives to the dark matter paradigm, aiming to explain galactic rotation curves, gravitational lensing, and large-scale cosmic structure without invoking unseen mass components. This review presents a mathematical perspective on the foundational models, focusing on formulations such as Modified Newtonian Dynamics (MOND), Tensor-Vector-Scalar theory (TeVeS), f (R) gravity, scalar-tensor theories, and higher-dimensional approaches like braneworld models. Using analytical tools rooted in differential geometry, variational principles, and nonlinear field equations, the review examines how modifications to the Einstein-Hilbert action alter geodesic behaviour, gravitational potentials, and structure formation dynamics. The mathematical consistency of each model particularly stability, ghost-free conditions, and well-posedness of field equations is critically assessed. Emphasis is placed on the derivation of modified Poisson equations, effective gravitational constants, and perturbation equations that influence cosmological evolution. The review further evaluates the ability of these theories to reproduce empirical observations such as the Tully-Fisher relation, Bullet Cluster gravitational lensing data, and cosmic microwave background anisotropies. Despite significant progress, many models face challenges including fine-tuning of free parameters, compatibility with solar system tests, and the emergence of higher-order instabilities. The paper concludes that while modified gravity offers mathematically elegant and conceptually innovative pathways to addressing mass discrepancies in the universe, no current theory fully resolves all observational and theoretical constraints. Continued development of mathematically robust frameworks, paired with high-precision astrophysical data, remains essential for assessing the viability of modified gravity as a true alternative to dark matter.
DOI: https://doi.org/10.22271/math.2025.v6.i2d.268
Pages: 694-698 | Views: 255 | Downloads: 105
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How to cite this article:
Deep Prabha Bharti. Modified gravity theories as alternatives to dark matter: A mathematical perspective. Journal of Mathematical Problems, Equations and Statistics. 2025; 6(2): 694-698. DOI: 10.22271/math.2025.v6.i2d.268
