concept

modified gravity

Modified gravity is a theoretical framework proposing alterations to general relativity to explain phenomena like galaxy rotation without dark matter.
15 related articles · 2 formulas · 6 who worked here

Description

Modified gravity — a class of theories proposing to change the law of gravitation on scales of galaxies and clusters, in order to explain the observed rotation without hypothetical dark matter. In standard cosmology, dark matter adds the missing mass; in alternative approaches, the geometry of spacetime or the potential itself is revised. The best-known model is MOND (Modified Newtonian Dynamics), introducing a threshold acceleration a₀ ≈ 1.2×10⁻¹⁰ m/s², below which the gravitational force transitions to a different regime.

History

The problem of missing mass was first noticed by Zwicky in 1933 in the Coma Cluster: the velocity dispersion of galaxies indicated a mass many times greater than the visible. In the 1970s, Vera Rubin systematically measured flat rotation curves of spiral galaxies, which were traditionally interpreted as evidence of a massive dark halo. In 1983, Mordehai Milgrom proposed MOND, which reproduced these curves without dark matter, introducing a single constant. Jacob Bekenstein in 2004 developed TeVeS — a relativistic extension of MOND, consistent with lensing and cosmology.

How it works

In the Newtonian limit F = G M m / r², but when a ≪ a₀ (typical value for galaxy outskirts) the effective force in MOND becomes F ≈ m a₀ / √(a/a₀) = m √(a₀ a). For a test body at distance r from central mass M, this yields v ≈ (G M a₀)^(1/4) — constant rotation velocity, explaining flat curves. In relativistic versions, the field equations are modified: instead of standard Einstein equations, additional metrics or scalars are introduced. The equivalence principle is usually preserved in the weak field. On galaxy cluster scales, even modified gravity often requires some amount of ordinary dark matter (e.g., sterile neutrinos).

In practice

Description of galaxy rotation without adding invisible mass; an alternative model for dark matter.

Fun fact

MOND accurately predicted the rotation curves of many galaxies, but it has not yet succeeded in explaining cluster collisions, as in the case of the Bullet Cluster.

Concept graph →

Formulas

$$a_0 = \frac{c^2}{\ell}$$
Characteristic acceleration scale in modified gravity.
What is in the formula
a_0variableCharacteristic acceleration scale — acceleration metre per second squared
cconstantSpeed of light in vacuum — speed of light = 299792458 metre per second
\ellconstantA characteristic length scale of the modified gravity theory — length scale metre
a_0=\frac{c^2}{\xi\ell_{\rmds}} · 2601.04290v1
$$F = -\frac{GMm}{r^2} - \frac{4\pi}{3} G m r \rho (1+3w)$$
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

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