Current State

Modified Newtonian Dynamics (MOND) and its relativistic generalizations have seen substantial theoretical development between 2022 and 2026, with a proliferation of scalar-tensor, vector-tensor, and nonlocal formulations aimed at coherently bridging galactic phenomenology and cosmological observables.

A key challenge remains constructing a single relativistic framework that simultaneously reproduces MOND at sub-galactic scales, recovers General Relativity (GR) at high accelerations, and matches cosmological data. The Khronon-Tensor theory of Blanchet and Skordis achieves precisely this: based on a Khronon scalar field foliated over spacelike hypersurfaces, it yields MOND dynamics for stationary galactic systems, recovers GR plus a cosmological constant in the strong-field regime, and is consistent with CMB anisotropies [AG-2025.07-019]. Similarly, Deffayet and Woodard present a nonlocal gravity model derived from corrections to the quantum gravitational stress tensor that interpolates between MOND behavior in gravitationally bound systems and full cosmological phenomenology—including the CMB, baryon acoustic oscillations, and linearized structure formation—within a single model [AG-2025.12-255].

Key Approaches

Scalar-field and Weyl geometric frameworks. Scholz constructs a Lagrangian model in integrable Weyl geometry incorporating a Bekenstein-type aquadratic term and a dynamical mass-generation term for a single scalar field. The aquadratic term recovers the deep-MOND (Newton–Milgrom) equation in the weak-field limit, while the mass term produces gravitational light deflection compatible with MOND free-fall trajectories. Crucially, the model activates only when the scalar field gradient is spacelike and below a MOND-typical threshold—analogous to the Berezhiani–Khoury superfluid mechanism—requiring a reexamination of the external field effect [AG-2025.10-400, AG-2025.10-399].

TeVeS and unit-timelike vector field theories. Domènech and Ganz demonstrate that any relativistic MOND model featuring a unit-timelike vector field—including TeVeS and Aether-scalar-tensor theory—can be embedded within a conformal/disformal-invariant framework. Gauge-fixing this symmetry recovers the norm constraint on the vector or scalar field, and these constraints are interchangeable provided fields remain timelike. This unification under mimetic gravity offers a systematic constructive principle for relativistic MOND via non-invertible disformal transformations [AG-2025.03-176].

Minimal relativistic MOND with gauge-sector motivation. Singh presents a minimal relativistic completion in which GR is recovered exactly in the high-acceleration regime while the Bekenstein–Milgrom (AQUAL) equation emerges in the low-acceleration limit, without introducing extra propagating fields. The construction is motivated by an E₆×E₆ framework; MOND is implemented via an IR metric deformation ΔS_IR[g] that is UV-vanishing, and the single MOND acceleration scale is set by a de Sitter radius: a₀ = c²/(ξ ℓ_dS) with ξ = O(1) [AG-2026.01-159].

Quantum gravity derivation. Pietrzyk et al. derive MOND from precanonical quantum gravity, showing that higher moments (third and fourth) of the geodesic equation with a random spin-connection term yield generalized qMOND potentials expressed in terms of Gauss and Appell hypergeometric functions, steeper interpolating functions, and a modified low-acceleration regime (mMOND) with asymptotic rotation curves ∝ r^{−1/18} [AG-2025.11-410].

Cosmological perturbation theory. Hwang and Noh present post-Newtonian (to 1PN order) and fully nonlinear relativistic perturbation equations for a relativistic MOND theory, finding that baryon perturbation grows faster in the MOND regime at 0PN order. They further show that the MOND field behaves as a fluid with a specific equation of state and no anisotropic stress, and derive a Jeans criterion for the MOND field [AG-2024.10-247].

Open Problems

The external field effect in scalar-field MOND models requires reexamination when dynamical mass generation is included [AG-2025.10-400]. Teleparallel and symmetric teleparallel gravity extensions, while cosmologically viable in some regimes, frequently fail Solar System bounds through deviations in the Eddington parameter, underscoring the difficulty of satisfying local and cosmological constraints simultaneously [AG-2025.11-174]. More broadly, ΛCdM tensions—Hubble constant discrepancy, growth rate anomalies, and anisotropies—remain motivators for modified gravity research without clear resolution [AG-2024.04-393].

Where to Read Next

For the theoretical unification of TeVeS-type theories with mimetic gravity, see [AG-2025.03-176]. For the most complete single-model treatment spanning galactic to cosmological scales, see [AG-2025.12-255] and [AG-2025.07-019]. Perturbation theory in the cosmological context is treated rigorously in [AG-2024.10-247], and the quantum gravity derivation of MOND interpolating functions is developed in [AG-2025.11-410].