Theoretical frameworks where dark matter effects are explained by modifications to gravitational laws.Modified gravity theories are alternative frameworks that seek to explain the observed effects attributed to dark matter without invoking an invisible particle. Instead of adding mass to galaxies and clusters, these theories modify the laws of gravity on large scales, such as by altering the inverse-square law or introducing additional fields. The most prominent example is Modified Newtonian Dynamics (MOND), which posits that gravitational acceleration deviates from Newtonian predictions below a certain threshold.
MOND was proposed by Mordehai Milgrom in 1983. Relativistic extensions were developed later, notably by Jacob Bekenstein in 2004 with TeVeS. The idea remains controversial, as it struggles to match observations of galaxy clusters and the cosmic microwave background without some form of dark matter.
In modified gravity, the gravitational force or the metric of spacetime is adjusted so that the rotation curves of galaxies flatten without extra mass. For instance, MOND introduces a characteristic acceleration scale below which gravity becomes stronger than Newtonian. Relativistic versions, like Tensor-Vector-Scalar (TeVeS) gravity, embed this idea into a full cosmological framework, aiming to reproduce gravitational lensing and cosmic expansion without dark matter.
Modified gravity theories are primarily used in theoretical cosmology and astrophysics to test alternatives to dark matter, guiding observational campaigns that look for deviations in gravitational lensing or galaxy dynamics.
Some modified gravity models predict that the gravitational field of a black hole could differ subtly from general relativity, potentially altering the shape of its shadow — an effect that could be tested with the Event Horizon Telescope.
| F | variable | Gravitational force magnitude — force newton |
| M | variable | Mass of the central object — mass kilogram |
| m | variable | Mass of the test particle — mass kilogram |
| r | variable | Distance between masses — distance metre |
| ρ | variable | Energy density of the cosmic fluid — energy density joule per cubic metre |
| w | variable | Equation-of-state parameter of the fluid — equation of state parameter |
| G | constant | Universal constant of gravitation — gravitational constant = 6.67430e-11 cubic metre per kilogram per second squared |
| E_n | variable | Perturbed energy of state n — energy joule |
| E_n^{(0)} | variable | Unperturbed energy of state n — energy joule |
| E_m^{(0)} | variable | Unperturbed energy of state m — energy joule |
| H' | variable | Perturbation Hamiltonian — hamiltonian joule |
| |n^{(0)}\rangle | variable | Unperturbed state n — quantum state |
| |m^{(0)}\rangle | variable | Unperturbed state m — quantum state |
| \sum_{m \neq n} | operator | Sum over all states m except n — summation |
| \langle m^{(0)} | H' | operator | Matrix element of perturbation between unperturbed states — matrix element |







