Modified gravity refers to any class of theoretical frameworks that alter or extend Albert Einstein's general theory of relativity - or, in some cases, Isaac Newton's law of universal gravitation - to account for observed astrophysical and cosmological phenomena without invoking undetected forms of matter or energy. The term encompasses a broad family of proposals ranging from modifications to the gravitational force law at low accelerations to higher-dimensional and scalar-tensor theories. Whether any such modification is physically correct, and which version best fits observational data, remains an open area of active research and dispute.

The principal motivation for modified gravity theories is the apparent mismatch between the predictions of standard gravitational theory and a range of astronomical observations. These include anomalous rotation curves of spiral galaxies, the dynamics of galaxy clusters, large-scale structure formation, and the observed accelerating expansion of the universe. Within the standard cosmological model (ΛCDM), these phenomena are attributed to dark matter and dark energy - entities whose fundamental nature has not been directly established. Modified gravity theories offer an alternative by positing that the gravitational law itself deviates from its standard form under certain conditions, such as very low accelerational regimes or at cosmological scales.

The two most studied families of modified gravity are:

Milgromian Dynamics (MOND) and its relativistic extensions. Proposed by Mordehai Milgrom in 1983, MOND postulates a modification to Newtonian dynamics below a characteristic acceleration scale (~1.2 × 10⁻¹⁰ m/s²).¹⁾ It has achieved notable predictive successes on galactic scales, particularly the baryonic Tully-Fisher relation and the radial acceleration relation. Relativistic completions of MOND include TeVeS (Tensor-Vector-Scalar gravity, developed by Jacob Bekenstein)²⁾ and more recent frameworks such as RMOND and covariant emergent gravity. The 2017 detection of gravitational waves from a neutron star merger (GW170817) and its electromagnetic counterpart imposed tight constraints on the propagation speed of gravitational waves, ruling out several relativistic MOND-adjacent theories and requiring surviving theories to be substantially revised.³⁾

f(R) and scalar-tensor theories. These modify the Einstein-Hilbert action by replacing the Ricci scalar R with a function f(R), or by coupling a scalar field to the metric.⁴⁾ They are primarily motivated by the dark energy problem and can produce late-time cosmic acceleration without a cosmological constant. Theories in this family include Brans-Dicke theory, Galileon gravity, and Horndeski theory (the most general scalar-tensor theory with second-order equations of motion). The GW170817 constraint likewise eliminated a large portion of Horndeski parameter space.⁵⁾

Other approaches include massive gravity, bigravity, extra-dimensional theories (such as the Dvali-Gabadadze-Porrati model), and emergent gravity proposals (such as those of Erik Verlinde).⁶⁾ Each carries distinct predictions, domains of applicability, and observational challenges.

Current observational tests span gravitational wave astronomy, precision solar system measurements, galaxy lensing surveys, cosmic microwave background analysis, and galaxy cluster dynamics. No single modified gravity framework has simultaneously and consistently reproduced all of these observations to the level of precision achieved by ΛCDM combined with general relativity, though proponents dispute how the comparison should be framed given the free parameters available to each framework. Interpretation of the evidence is contested; see modified-gravity-debate-mond-vs-dark-matter-debate and modified-gravity-controversy-gw170817-constraints-controversy.

There is broad consensus among researchers across multiple institutions that general relativity is accurate within the solar system and in the strong-field regime tested by gravitational wave observations. This consensus does not, by itself, resolve the question of whether gravity is modified at galactic or cosmological scales, since those regimes probe different acceleration and curvature conditions than solar system tests. See modified-gravity-consensus-general-relativity-precision-tests-consensus.

No comparable independent consensus exists on whether any specific modified gravity theory correctly describes galactic or cosmological dynamics. The field remains in active contention.

* Modified gravity as the correct account of galactic dynamics - Proponents, particularly of MOND-based frameworks, argue that the empirical regularities on galactic scales (the radial acceleration relation, the baryonic Tully-Fisher relation) are most naturally explained by a modification of gravity rather than by positing unseen matter. modified-gravity-mond-preferred-viewpoint

* Dark matter within standard gravity as the correct account - The dominant view in contemporary cosmology holds that the observational data are better explained by cold dark matter particles within general relativity, pointing to structure formation, the cosmic microwave background power spectrum, and the Bullet Cluster observations as cases where MOND and its extensions struggle. modified-gravity-dark-matter-preferred-viewpoint

* Modified gravity as a complement to, rather than replacement for, dark matter - Some researchers propose that both some form of dark matter and a modification of gravity may be required; or that dark matter particles themselves may generate an effective MOND-like phenomenology through their distribution. modified-gravity-hybrid-approach-viewpoint

* Emergent gravity - A distinct class of proposals, associated with work by Verlinde and others, treats gravity as an emergent thermodynamic phenomenon rather than a fundamental force, with modifications arising from the entropic structure of spacetime. Emergent Gravity - Emergent Gravity Viewpoint

* Skepticism toward all current modified gravity proposals - Some physicists and cosmologists hold that existing modified gravity theories are insufficiently developed, lack predictive power at all relevant scales, or have been empirically falsified by GW170817 and other observations, and that the standard ΛCDM framework - despite the unresolved nature of dark matter and dark energy - remains the only viable framework pending direct dark matter detection. modified-gravity-skeptical-viewpoint

* GW170817 and the viability of relativistic MOND extensions - The 2017 gravitational wave event imposed constraints that eliminated or severely restricted several relativistic completions of MOND; proponents dispute whether these constraints rule out the broader MOND research program or only specific implementations. modified-gravity-controversy-gw170817-constraints-controversy

* The Bullet Cluster as a test case - The Bullet Cluster (1E 0657-558) is widely cited as evidence favoring dark matter over modified gravity;⁷⁾ advocates of modified gravity dispute this interpretation, particularly for MOND extensions incorporating sterile neutrinos or other auxiliary matter. modified-gravity-controversy-bullet-cluster-controversy

* modified-gravity-history * modified-gravity-debate-mond-vs-dark-matter-debate * modified-gravity-mond-preferred-viewpoint * modified-gravity-dark-matter-preferred-viewpoint * modified-gravity-hybrid-approach-viewpoint * Emergent Gravity - Emergent Gravity Viewpoint * modified-gravity-skeptical-viewpoint * modified-gravity-consensus-general-relativity-precision-tests-consensus * modified-gravity-controversy-gw170817-constraints-controversy * modified-gravity-controversy-bullet-cluster-controversy * Dark Matter * Dark Energy * General Relativity * cosmological-standard-model

1. Milgrom, Mordehai. “A Modification of the Newtonian Dynamics as a Possible Alternative to the Hidden Mass Hypothesis.” The Astrophysical Journal 270 (1983): 365-370. https://doi.org/10.1086/161130. 2. Bekenstein, Jacob D. “Relativistic Gravitation Theory for the Modified Newtonian Dynamics Paradigm.” Physical Review D 70, no. 8 (2004): 083509. https://doi.org/10.1103/PhysRevD.70.083509. 3. Abbott, B. P., et al. “GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral.” Physical Review Letters 119, no. 16 (2017): 161101. https://doi.org/10.1103/PhysRevLett.119.161101. 4. Sotiriou, Thomas P., and Valerio Faraoni. “f(R) Theories of Gravity.” Reviews of Modern Physics 82, no. 1 (2010): 451-497. https://doi.org/10.1103/RevModPhys.82.451. 5. Creminelli, Paolo, and Filippo Vernizzi. “Dark Energy after GW170817 and GRB170817A.” Physical Review Letters 119, no. 25 (2017): 251302. https://doi.org/10.1103/PhysRevLett.119.251302. 6. Verlinde, Erik P. “Emergent Gravity and the Dark Universe.” SciPost Physics 2, no. 3 (2017): 016. https://doi.org/10.21468/SciPostPhys.2.3.016. 7. Clowe, Douglas, et al. “A Direct Empirical Proof of the Existence of Dark Matter.” The Astrophysical Journal Letters 648, no. 2 (2006): L109-L113. https://doi.org/10.1086/508162.