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MOND, Original Phenomenological Law vs TeVeS (Tensor-Vector-Scalar)

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	MOND, Original Phenomenological Law Frontier	TeVeS (Tensor-Vector-Scalar) Frontier
Proposed	1983	2004
Key figures	Mordehai Milgrom, Stacy McGaugh, Federico Lelli	Jacob Bekenstein
In one sentence	Milgrom proposed in 1983 that Newton's law of gravity breaks down at extremely low accelerations, below a universal scale a_0 ≈ 10^-10 m/s². Below this scale, gravity effectively gets stronger than Newton predicts, and galaxies rotate as observed without invoking dark matter.	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.
Predictions	Radial acceleration relation: in every galaxy, how fast stars actually accelerate as they orbit is fixed by how much visible matter is present. The observed centripetal acceleration (the inward pull that keeps an orbit curving) tracks the Newtonian acceleration predicted from baryonic matter (ordinary stars and gas) through one universal scale a_0, with no separate dark-halo parameter tuned per galaxy The baryonic Tully-Fisher relation: a spinning galaxy's flat rotation speed to the fourth power tracks its visible (baryonic) mass, V^4 ∝ M_baryon · a_0, with none of the scatter you would expect if dark-halo properties varied, because in MOND there is no halo Wide binaries at separations above ~10^4 AU have orbital velocities probing the deep-MOND regime; specific Newton-Kepler deviations are predicted	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)
Where it breaks	Clowe et al 2006 Bullet Cluster: weak-lensing mass is spatially separated from baryonic gas after a cluster collision, requiring some dark component beyond what MOND alone provides CMB acoustic-peak structure is fit precisely by ΛCDM with cold dark matter; no MOND-derived cosmological framework reproduces the CMB without invoking some particle-like dark component Pittordis & Sutherland 2022 wide-binary analysis using Gaia EDR3 found a preference for GR over MOND, contradicting earlier claims of MOND-like tension; subsequent analyses are ongoing Galaxy cluster dynamics (X-ray temperature profiles, lensing mass) require more mass than baryons alone, even in MOND, undercutting the 'no dark matter' motivation at cluster scales MOND has no fundamental motivation: a_0 is fit empirically, not derived from first principles, and the interpolating function between Newtonian and deep-MOND regimes is also free-form	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
Key unresolved problem	The cluster-scale failure: MOND fits single galaxies beautifully, but in galaxy clusters like the Bullet Cluster the bending of light reveals far more mass than the visible matter and MOND together can explain, so some hidden dark component still seems necessary.	The gravitational-wave speed problem: the 2017 GW170817 event showed gravity travels at the speed of light, yet most versions of TeVeS make gravitational waves travel at a different speed, so the theory survives only with heavy fine-tuning.
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MOND, Original Phenomenological Law

1983 · Frontier

TeVeS (Tensor-Vector-Scalar)

2004 · Frontier

Proposed

1983

2004

Key figures

Mordehai Milgrom, Stacy McGaugh, Federico Lelli

Jacob Bekenstein

In one sentence

Milgrom proposed in 1983 that Newton's law of gravity breaks down at extremely low accelerations, below a universal scale a_0 ≈ 10^-10 m/s². Below this scale, gravity effectively gets stronger than Newton predicts, and galaxies rotate as observed without invoking dark matter.

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.

Predictions

Radial acceleration relation: in every galaxy, how fast stars actually accelerate as they orbit is fixed by how much visible matter is present. The observed centripetal acceleration (the inward pull that keeps an orbit curving) tracks the Newtonian acceleration predicted from baryonic matter (ordinary stars and gas) through one universal scale a_0, with no separate dark-halo parameter tuned per galaxy
The baryonic Tully-Fisher relation: a spinning galaxy's flat rotation speed to the fourth power tracks its visible (baryonic) mass, V^4 ∝ M_baryon · a_0, with none of the scatter you would expect if dark-halo properties varied, because in MOND there is no halo
Wide binaries at separations above ~10^4 AU have orbital velocities probing the deep-MOND regime; specific Newton-Kepler deviations are predicted

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)

Where it breaks

Clowe et al 2006 Bullet Cluster: weak-lensing mass is spatially separated from baryonic gas after a cluster collision, requiring some dark component beyond what MOND alone provides
CMB acoustic-peak structure is fit precisely by ΛCDM with cold dark matter; no MOND-derived cosmological framework reproduces the CMB without invoking some particle-like dark component
Pittordis & Sutherland 2022 wide-binary analysis using Gaia EDR3 found a preference for GR over MOND, contradicting earlier claims of MOND-like tension; subsequent analyses are ongoing
Galaxy cluster dynamics (X-ray temperature profiles, lensing mass) require more mass than baryons alone, even in MOND, undercutting the 'no dark matter' motivation at cluster scales
MOND has no fundamental motivation: a_0 is fit empirically, not derived from first principles, and the interpolating function between Newtonian and deep-MOND regimes is also free-form

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

Key unresolved problem

The cluster-scale failure: MOND fits single galaxies beautifully, but in galaxy clusters like the Bullet Cluster the bending of light reveals far more mass than the visible matter and MOND together can explain, so some hidden dark component still seems necessary.

The gravitational-wave speed problem: the 2017 GW170817 event showed gravity travels at the speed of light, yet most versions of TeVeS make gravitational waves travel at a different speed, so the theory survives only with heavy fine-tuning.

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