
Theories altering general relativity to explain dark energy or matter.Modified gravity theories are a family of alternative descriptions of gravity that depart from Einstein's general relativity. They are primarily proposed to explain cosmic acceleration (dark energy) or the dynamics of galaxies and clusters without invoking invisible dark matter. Instead of adding new substances to the universe, these theories modify the laws of gravity themselves, often by adding extra fields, changing the number of dimensions, or altering the Einstein-Hilbert action.
The idea of modifying gravity dates back to the early 20th century, but modern interest surged in the late 1990s after the discovery of cosmic acceleration. Notable early proposals include Brans-Dicke theory (1961) and later f(R) theories, which gained prominence in the 2000s as alternatives to the cosmological constant.
In general relativity, gravity is the curvature of spacetime caused by mass and energy. Modified theories change this relationship. For example, f(R) gravity replaces the Ricci scalar R in the action with a more complex function f(R), introducing new degrees of freedom that can mimic dark energy. Other approaches add a fifth dimension (as in braneworld scenarios) or introduce a massive graviton, altering how gravity behaves at large distances or in strong fields.
Modified gravity theories are tested using gravitational wave observations, galaxy cluster dynamics, and cosmic microwave background data. They are also used in cosmological simulations to predict observable signatures that distinguish them from dark energy models.
Some modified gravity theories predict that gravitational waves travel at slightly different speeds than light, a prediction that was tightly constrained by the 2017 neutron star merger GW170817.
| a_0 | variable | Characteristic acceleration scale — acceleration metre per second squared |
| c | constant | Speed of light in vacuum — speed of light = 299792458 metre per second |
| \ell | constant | A characteristic length scale of the modified gravity theory — length scale metre |
| 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 |




