concept

modified gravity theories

Theories altering general relativity to explain dark energy or matter.
13 related articles · 3 formulas

Description

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.

History

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.

How it works

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.

In practice

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.

Fun fact

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.

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
$$E_n \approx E_n^{(0)} + \sum_{m \neq n} \frac{|\langle m^{(0)} | H' | n^{(0)} \rangle|^2}{E_n^{(0)} - E_m^{(0)}}$$
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

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