concept

dark matter modified gravity

Theoretical frameworks where dark matter effects are explained by modifications to gravitational laws.
13 related articles · 2 formulas

Description

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.

History

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.

How it works

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.

In practice

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.

Fun fact

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.

Concept graph →

Formulas

$$F = -\frac{GMm}{r^2} - \frac{4\pi}{3} G m r \rho (1+3w)$$
Gravitational force modified by dark energy pressure, vanishes at w=-1/3.
What is in the formula
FvariableGravitational force magnitude — force newton
MvariableMass of the central object — mass kilogram
mvariableMass of the test particle — mass kilogram
rvariableDistance between masses — distance metre
ρvariableEnergy density of the cosmic fluid — energy density joule per cubic metre
wvariableEquation-of-state parameter of the fluid — equation of state parameter
GconstantUniversal constant of gravitation — gravitational constant = 6.67430e-11 cubic metre per kilogram per second squared
f=-\frac{gmm}{r^2}-\frac{4π}{3}gmrρ(1+3w) · 2605.13705v1
$$E_n \approx E_n^{(0)} + \sum_{m \neq n} \frac{|\langle m^{(0)} | H' | n^{(0)} \rangle|^2}{E_n^{(0)} - E_m^{(0)}}$$
Energy correction from summing over matrix elements divided by energy differences.
What is in the formula
E_nvariablePerturbed energy of state n — energy joule
E_n^{(0)}variableUnperturbed energy of state n — energy joule
E_m^{(0)}variableUnperturbed energy of state m — energy joule
H'variablePerturbation Hamiltonian — hamiltonian joule
|n^{(0)}\ranglevariableUnperturbed state n — quantum state
|m^{(0)}\ranglevariableUnperturbed state m — quantum state
\sum_{m \neq n}operatorSum over all states m except n — summation
\langle m^{(0)} | H'operatorMatrix element of perturbation between unperturbed states — matrix element
e_i\approxe_i^{(0)}+\sum_{i'}\frac{t_{pd}^2}{e_i^{(0)}-e_{i'}^{(0)}} · 2607.03022

Related articles · 13

General Relativity2026-07-281 minarXiv:2607.25311express
How Black Holes Ring After a Strike
A stone falls into still water — ripples spread across the surface. A black hole behaves similarly when something falls into it or when it merges with another black hole. The hole begins to oscillate, and these oscillations propagate through space as gravitational waves.
Galaxies2026-07-163 minarXiv:2607.14450
Invisible Gravity: The Dance of Double Stars Challenges Newton
Two figure skaters on a lake frozen to the horizon. They are so far apart that their silhouettes turn into dots, and their mutual attraction becomes almost an article of faith. By Newton's law, they should circle in an unimaginably slow waltz. But telescopes see otherwise.
Cosmology2026-07-143 minarXiv:2607.12745
The Chameleon Universe: How Gravity Learns to Hide
In the depths of space, gravity is mastering the art of disguise. For a quarter century, astrophysicists have been trying to decipher the nature of dark energy, which makes the Universe expand at an accelerating rate.
General Relativity2026-07-111 minarXiv:2607.10247express
Gravity Looks Sideways
A lead sphere hangs above another lead sphere. According to the usual laws of gravitation, they attract each other exactly along the vertical — along the line connecting their centers.
General Relativity2026-06-191 minarXiv:2606.21019express
How to Hear the Warmth of the Void
The vacuum is not as empty as it seems. If an observer moves with acceleration, the vacuum around them heats up: this was predicted by William Unruh back in the 1970s. The effect is akin to black hole radiation, but in flat space.
HEP Phenomenology2026-06-101 minarXiv:2606.12546express
Magnetars as Gravitational Echoes
A dead star with a magnetic field billions of times stronger than Earth's is a magnetar. Its crust cracks, sending a powerful X-ray burst into space. But some of that light doesn't reach us in its usual form. In an ultra-strong field, photons can turn into gravitational waves — the trembling of space itself.
Galaxies2026-05-112 minarXiv:2605.10857express
Dark Matter vs. Modified Gravity: A Verdict from Stellar Kinematics
A galaxy is like a cosmic highway where stars, like cars, race along circular orbits. Their speed is set by the invisible "cargo" of mass enclosed within the orbit: the more massive the central region, the faster the stars at the periphery.
General Relativity2026-05-041 minarXiv:2605.02807express
How Particle Clouds Bend Light Rays
When light swings past a massive body like a black hole, its path warps — an effect predicted by Einstein. New research has taken into account that near such objects, clouds of hadrons often swirl — the very particles we know from protons and neutrons in atomic nuclei.
General Relativity2026-04-171 minarXiv:2604.15965express
Dancing Black Holes Put the Universe's Geometry to the Test
The merger of two black holes is like a dance that ends in a powerful burst — a gravitational wave. This wave carries the imprint of how spacetime is curved around the objects. If the geometry differed from what we're used to, as if a ball rolled not on a flat floor but on wavy linoleum, the signal would be different.
Cosmology2026-02-252 minarXiv:2602.21774express
Dark Matter on the Scales of Gravity
In the dark depths of space lurks invisible matter. It doesn't shine, but its pull holds galaxies together. Usually, we assume dark matter obeys the same laws of gravity as tables and chairs. A new study offers a different perspective: dark matter might subtly alter gravity itself.
General Relativity2026-01-071 minarXiv:2601.04290express
How Weak Gravity Does Without Dark Matter
Astronomers, including Vera Rubin, noticed that stars on the outskirts of galaxies rotate faster than visible mass allows. To explain this, they invented dark matter — an invisible ballast. But there's another possibility: gravity isn't always the same.
General Relativity2026-01-051 minarXiv:2601.01715express
Gravity Without Dark Matter: The Entropic Approach Triumphs
In tiny satellite galaxies, stars on the outskirts rotate faster than visible matter allows. It’s as if a pattern appears on the fabric of space for which there aren’t enough threads.
Quantum Gases2026-01-031 minarXiv:2601.01039express
How quantum fog tests the laws of gravity
An ultracold atomic cloud, resembling fog, hints that gravity might not work as Newton said. On the outskirts of galaxies stars move faster than expected, and MOND theory tweaks the law of gravitation over large distances, removing the need for dark matter.