In this article, straightforward alternatives to general relativity are discussed, which do not involve quantum mechanics or force unification.
However, some of the alternative theories of gravity are supported by a minority of physicists, and the topic remains the subject of intense study in theoretical physics.
Canonical methods provide another way to construct systems that have the required conservation laws, but this approach is more cumbersome to implement.
of signature (−, +, +, +), which governs proper-length and proper-time measurements in the usual manner of special and general relativity: where there is a summation over indices
[20] Scalar–Tensor theories include Thiry,[20] Jordan,[24] Brans and Dicke,[9] Bergman,[36] Nordtveldt (1970), Wagoner,[39] Bekenstein[47] and Barker.
The above examples are particular cases of Horndeski's theory,[58][59] the most general Lagrangian constructed out of the metric tensor and a scalar field leading to second order equations of motion in 4-dimensional space.
Independently of Cartan, similar ideas were put forward by Sciama, by Kibble in the years 1958 to 1966, culminating in a 1976 review by Hehl et al.
The original description is in terms of differential forms, but for the present article that is replaced by the more familiar language of tensors (risking loss of accuracy).
This section includes alternatives to general relativity published after the observations of galaxy rotation that led to the hypothesis of "dark matter".
The basic idea is that gravity agrees with general relativity at the present epoch but may have been quite different in the early universe.
led to the general acceptance that it is zero, but the use of a non-zero value came back when data from supernovae indicated that the expansion of the universe is accelerating.
is an arbitrary function of the scalar field rather than a constant, it can be set to give an acceleration that is large in the early universe and small at the present epoch.
In December 2018, the astrophysicist Jamie Farnes from the University of Oxford proposed a dark fluid theory, related to notions of gravitationally repulsive negative masses that were presented earlier by Albert Einstein.
The theory will be directly testable using the world's largest radio telescope, the Square Kilometre Array which should come online in 2022.
MOND successfully explains the Tully–Fisher observation that the luminosity of a galaxy should scale as the fourth power of the rotation speed.
A relativistic version of this based on scalar–tensor theory was rejected because it allowed waves in the scalar field to propagate faster than light.
By 1988, a second scalar field (PCC) fixed problems with the earlier scalar–tensor version but is in conflict with the perihelion precession of Mercury and gravitational lensing by galaxies and clusters.
Haugan and Kauffmann[78] used polarization measurements of the light emitted by galaxies to impose sharp constraints on the magnitude of some of nonsymmetric gravitational theory's parameters.
In order to remove ghosts in the modified propagator, as well as to obtain asymptotic freedom, Biswas, Mazumdar and Siegel (2005) considered a string-inspired infinite set of higher derivative terms where
[79][80] This avoids a black hole singularity near the origin, while recovering the 1/r fall of the general relativity potential at large distances.
The interaction between gluons emitted by static or nearly static quarks dramatically strengthens quark-quark interaction, ultimately leading to quark confinement on the one hand (analogous to the need of stronger gravity to explain away dark matter) and the suppression of the Strong Nuclear Force outside hadrons (analogous to the repulsion of dark energy that balances gravitational attraction at large scales.)
Two other parallel phenomena are the Tully-Fisher relation in galaxy dynamics that is analogous to the Regge trajectories emerging from the strong force.
As an example of disagreement with Newtonian experiments, Birkhoff[18] theory predicts relativistic effects fairly reliably but demands that sound waves travel at the speed of light.
For example, the non-metric theory of Belinfante & Swihart[26][27] is eliminated by the THεμ formalism for testing Einstein's Equivalence Principle.
After the multi-messaging detection of the GW170817 coalescence of neutron stars, where light and gravitational waves were measured to travel at the same speed with an error of 1/1015, many of those modified theories of gravity were excluded.
For those theories that aim to replace inflation, the size of ripples in the spectrum of the cosmic microwave background radiation is the strictest test.
For those theories that incorporate or aim to replace dark energy, the supernova brightness results and the age of the universe can be used as tests.
Misner et al.[52] gives a table for translating parameters from the notation of Ni to that of Will) General Relativity is now more than 100 years old, during which one alternative theory of gravity after another has failed to agree with ever more accurate observations.
All experimental tests agree with general relativity so far, and so Parametric post-Newtonian analysis immediately eliminates all the scalar field theories in the table.
Non-metric theories, such as Belinfante and Swihart,[26][27] usually fail to agree with experimental tests of Einstein's equivalence principle.