The first relativistic MOND theory. Adds scalar and vector fields to gravity.
TeVeS (Tensor-Vector-Scalar)
A relativistic theory that reduces to MOND in weak fields and GR in strong fields by adding scalar and vector fields to the metric. GW170817 constraints have substantially limited it.
Looping ambient scene for Modified Gravity / MOND. Modified-gravity programs share a single editorial commitment: instead of postulating invisible particles (dark matter) or a cosmological term (dark energy), modify general relativity at the scales where ΛCDM invokes them. MOND's original observation is that galaxy rotation curves obey a tight phenomenological law tied to a universal acceleration scale a_0 ≈ 10^-10 m/s². This pattern is too clean to be coincidence and is not derived from first principles by ΛCDM. The hard part is extending the same idea to clusters, the CMB, and large-scale structure. Whether the same principle scales to clusters and cosmology is the open empirical question. Cluster and cosmological data favor ΛCDM cleanly; galaxy-scale data favor MOND-style patterns just as cleanly. Both empirical signals are real.
§1 · The claim, in one sentence
Bekenstein's 2004 TeVeS is a relativistic theory that reduces to MOND in weak fields and to general relativity in strong fields, by adding a scalar and a vector field to the metric. It was the first serious relativistic MOND, but GW170817 constraints have substantially limited it.
§2 · Why it might be true
Bekenstein 2004 proposed TeVeS as a relativistic upgrade of MOND. The metric tensor of general relativity is supplemented by a scalar field and a unit-norm vector field; together these fields produce MOND-like behavior at low accelerations, GR-like behavior at high accelerations, and remain mathematically consistent under general coordinate transformations. The theory was constructed to handle the things non-relativistic MOND cannot: gravitational lensing, cosmological perturbations, and the propagation of gravitational waves.
GW170817 changed the landscape. In August 2017, LIGO detected gravitational waves from a binary neutron-star merger (GW170817) and the same event was observed in gamma rays within 1.7 seconds. This constrains the speed of gravitational waves to match the speed of light to roughly 1 part in 10^15. Generic TeVeS configurations predict tensor modes propagating at speeds different from light, because the vector field couples to tensor perturbations in a way that generically modifies their propagation speed. Matching GW170817 requires either fine-tuning the theory's parameters or significant modifications to its field content.
TeVeS remains studied as a historically important relativistic-MOND case study and continues to be useful for cluster-lensing analysis. The active research line has moved to newer frameworks (Skordis-Złośnik, the next variant) constructed to be compatible with GW170817 from the start.
The family stance
Galaxies don't need invisible matter; they need modified gravity at low accelerations. The radial acceleration relation is real and tight, and any successful theory of the dark sector must reproduce it. Whether the same principle scales to clusters and cosmology is the open empirical question. Cluster and cosmological data favor ΛCDM cleanly; galaxy-scale data favor MOND-style patterns just as cleanly. Both empirical signals are real.
§2.5 · Evidence
- In the low-gravity limit TeVeS recovers MOND's galaxy-scale successes, including the tight radial acceleration relation seen in real rotation curves
- TeVeS can actually compute how much light a galaxy or cluster bends, the lensing predictions needed to confront observations like the Bullet Cluster, which non-relativistic MOND alone cannot produce
§3 · What you'd need to test it
- How much background light a galaxy or cluster bends (gravitational lensing) should follow the TeVeS values set by the visible matter alone, not the larger ΛCDM values that assume a dark-matter halo; the cleanest test is the ratio of lensing mass to ordinary (baryonic) mass in colliding clusters
- The acoustic peaks in the cosmic microwave background, the regular ripples left by sound waves in the early universe, should come out with different heights and spacings than ΛCDM predicts, testable against Planck satellite data
- Tensor mode propagation speed potentially different from light speed (now tightly constrained by GW170817)
§4 · Where it breaks
- GW170817 constrains tensor mode propagation speed to match light speed to one part in 10^15; generic TeVeS configurations violate this and require fine-tuning to survive
- Cosmological perturbation analyses find TeVeS struggles to reproduce the CMB acoustic peaks and large-scale structure formation as well as ΛCDM
- The theory's field content (scalar plus vector plus free interpolating functions) is seen as baroque relative to ΛCDM's simplicity
- Active relativistic-MOND research has moved to newer frameworks (Skordis-Złośnik) that handle GW170817 from the start, leaving TeVeS as a reference rather than a live candidate
Go deeper
TeVeS field content: a physical metric g_μν, a unit timelike vector field U_μ with g_μν U^μ U^ν = -1, and a scalar field φ. The physical metric is related to the Einstein-frame metric by a disformal transformation involving φ and U_μ; this is what produces MOND-like behavior in the appropriate limit.
Bekenstein's original construction included a free function F that determines the strength of the scalar field's effect on the dynamics. Choosing F appropriately gives MOND in the deep-MOND regime and GR in the high-acceleration regime.
GW170817 specifically: in TeVeS, tensor perturbations to the metric have propagation speed c_T^2 = 1 / (1 - 2 σ_TeVeS), where σ_TeVeS depends on the vector field configuration. To match c_T = c required by GW170817, σ_TeVeS must be extremely small, fine-tuning the theory's parameter space.
Cosmological context: TeVeS perturbation equations differ from ΛCDM. Reproducing the third and higher CMB acoustic peaks requires additional ingredients (often a hot dark matter component) that undercut the original 'no dark matter needed' motivation.
▸§5 · Who built it, and when(2 sources, 2 established)
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