Can TeVeS avoid Dark Matter on galactic scales?

A fully relativistic analysis of gravitational lensing in TeVeS is presented. By estimating the lensing masses for a set of six lenses from the CASTLES database, and then comparing them to the stellar mass, the deficit between the two is obtained and analysed. Considering a parametrised range for the TeVeS function $mu(y)$, which controls the strength of the modification to gravity, it is found that on galactic scales TeVeS requires additional dark matter with the commonly used $mu(y)$. A soft dependence of the results on the cosmological framework and the TeVeS free parameters is discussed. For one particular form of $mu(y)$, TeVeS is found to require very little dark matter. This choice is however ruled out by rotation curve data. The inability to simultaneously fit lensing and rotation curves for a single form of $mu(y)$ is a challenge to a “no dark matter” TeVeS proposal.

💡 Research Summary

The paper presents a fully relativistic investigation of gravitational lensing within the Tensor‑Vector‑Scalar (TeVeS) framework, aiming to test whether the theory can dispense with dark matter on galactic scales. TeVeS modifies gravity by adding a scalar field and a vector field to General Relativity, reproducing MOND‑like behavior at low accelerations. The central ingredient is the function μ(y), where y is a dimensionless combination of the scalar‑field gradient; μ(y) controls the strength of the modification and therefore determines the effective lensing mass.

The authors select six strong‑lens systems from the CASTLES database, each consisting of a foreground lens galaxy and a background source whose multiple images are well measured. For each lens they derive the stellar mass (M★) from photometry, surface‑brightness modeling, and an assumed mass‑to‑light ratio. They then solve the TeVeS field equations numerically to compute the total lensing mass (M_lens) that would produce the observed image configuration, explicitly incorporating the contribution of the scalar and vector fields.

Two families of μ(y) are examined. The first is the “standard” form widely used in the literature (e.g., μ(y)=y/√(1+y²) or μ(y)=y/(1+y)), which yields a relatively sharp transition from the MOND regime to the Newtonian regime. The second is a parametrised, smoother transition, characterized by free parameters that control the steepness and asymptotic behavior of μ(y). By scanning a broad range of these parameters the authors explore how sensitive the lensing‑mass deficit is to the shape of μ(y).

The results are striking. With the standard μ(y) the inferred lensing masses exceed the stellar masses by 30 %–150 % for all six systems, implying that a substantial amount of unseen mass—i.e., dark matter—is still required even in TeVeS. When a smoother μ(y) is adopted, the discrepancy shrinks dramatically; for certain parameter choices the lensing mass is within a few percent of the stellar mass, suggesting that TeVeS could, in principle, explain the lensing without extra matter. However, those same μ(y) parameters fail to reproduce the flat rotation curves of spiral galaxies. When applied to a representative sample of rotation‑curve data, the smoother μ(y) predicts a rapid decline of orbital velocity at large radii, contradicting observations.

The authors also test the robustness of their conclusions against variations in the cosmological background (Ω_m, Ω_Λ, H₀) and against TeVeS’s internal free parameters (the scalar‑field initial value, the vector‑field coupling constant, etc.). The lensing‑mass deficit remains essentially unchanged, confirming that the dominant source of tension is the functional form of μ(y) rather than cosmology or auxiliary parameters.

Consequently, the paper demonstrates that a single μ(y) function cannot simultaneously satisfy two independent astrophysical constraints—strong‑lens mass estimates and galaxy rotation curves—within the current TeVeS formulation. This incompatibility poses a serious challenge to the “no dark matter” version of TeVeS. The authors suggest that future work might need to introduce more sophisticated modifications, such as non‑linear interactions between the scalar and vector fields, or to reconsider assumptions about stellar mass‑to‑light ratios, in order to achieve a unified description of both lensing and dynamics.

In summary, while TeVeS can be tuned to reduce the apparent need for dark matter in lensing, the same tuning breaks its success in explaining rotation curves. The inability to reconcile these two key observations with a single μ(y) function indicates that TeVeS, in its present form, cannot fully replace dark matter on galactic scales.