Alternatives to general relativity

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Alternatives to General Relativity: a concise, easy-to-understand guide

What these theories try to do
- General relativity (GR) is our best description of gravity, but some puzzles in cosmology and astrophysics have led physicists to explore other gravity theories.
- No alternative has become the standard model of gravity yet. GR has passed many tests across a wide range of masses and sizes, and new observations continue to support it, but mysteries like dark matter and dark energy keep the discussion alive.

How these theories are organized
- Metric theories: gravity is described by a space-time metric that tells matter how to move. GR is the best-known example, but many alternatives modify or extend the metric approach.
- Non-metric theories: gravity is described without relying on a space-time metric in the usual way. These often involve additional fields or different mathematical structures.
- Extra fields: many alternative theories add one or more new fields to gravity:
- Scalar fields (scalar-tensor theories)
- Vector fields (vector-tensor theories)
- Both scalar and vector fields (tensor-scalar-vector theories)
- Other approaches include modifying the action that describes gravity, introducing multiple metrics (bimetric theories), or adding higher-order terms or extra dimensions.
- Some modern ideas aim to replace dark matter or dark energy with changes to gravity, while others keep GR but add elements like a cosmological constant or a scalar potential.

Some well-known families and ideas
- Scalar-tensor theories (e.g., Brans-Dicke): gravity is described by a metric plus a scalar field that can change the effective strength of gravity.
- Vector-tensor theories: add a vector field to gravity, sometimes implying a preferred frame of reference.
- Bimetric and non-metric approaches: use two metrics or a different underlying structure to describe gravity.
- Higher-curvature and modified-action theories (e.g., f(R) gravity, Starobinsky gravity, Gauss–Bonnet, Lovelock): modify the gravitational action to include extra curvature terms.
- MOND and relativistic MOND (RAQUAL, TeVeS): proposed to explain galaxy rotation curves without dark matter; TeVeS adds tensors, vectors, and scalars to try to reproduce MOND in a relativistic setting.
- Moffat’s theories (MSTG, MOG) and other non-GR models: introduce extra fields to explain rotation curves and lensing without invoking dark matter.
- Non-symmetric gravity and Einstein–Cartan ideas: allow torsion or non-symmetric structures in the gravitational field.
- Gravitational self-interaction ideas (GRSI) and related concepts: try to explain observations by adding self-interaction terms within gravity itself.
- Some theories aim to explain cosmology with a different kind of fluid or scalar/vector fields that mimic dark energy or dark matter.

How these theories are tested
- Classical tests: redshift, light bending, gravitational lensing, and the advance of planetary orbits. Any viable theory must reproduce GR’s success in these areas.
- Weak-field tests: the Parametric Post-Newtonian (PPN) framework compares how theories deviate from Newtonian gravity in the solar system. GR matches the data very well; many alternatives are tightly constrained or ruled out by these tests.
- Strong-field tests: observations of neutron stars, white dwarfs, black holes, and binary pulsars probe gravity in extreme conditions.
- Gravitational waves: the speed and properties of gravitational waves test how gravity behaves in dynamic, strong-field events. The GW170817 event showed gravitational waves travel at the speed of light to incredible precision, ruling out many alternative theories that predict different speeds.
- Cosmology: the large-scale structure of the universe, galaxy rotation curves, the cosmic microwave background, and the expansion history constrain how gravity acts over vast distances and times.
- In short: any viable alternative must be consistent with a wide range of observations, from solar system experiments to cosmology.

Why this matters for cosmology
- Dark matter and dark energy are central parts of the standard cosmology that uses GR. Some alternative theories try to explain these phenomena by modifying gravity instead of introducing unknown matter or energy.
- Other ideas keep GR but add a cosmological constant, quintessence, or “dark fluids” to match observations in the early and late universe.
- The choice between modifying gravity and adding new forms of matter/energy is still an active area of research. Observations, especially of gravitational waves and precise cosmological measurements, keep narrowing the possibilities.

Bottom line
- General relativity remains the most successful theory of gravity we have, supported by a century of experiments and observations.
- A variety of alternative theories exist, each with different motivations and predictions. So far, none has replaced GR, but these ideas help scientists test the limits of gravity and explore whether new physics might be revealed in extreme environments or the early universe.
- Ongoing and future observations across astronomy, gravitational waves, and cosmology will continue to test these theories and sharpen our understanding of gravity.