Modified Gravity and the Dark-Matter Alternative

Low-acceleration modified dynamics organizes several striking galaxy regularities with a characteristic acceleration scale, and covariant theories can reproduce important parts of that phenomenology. The stronger replacement claim is not established: one fixed relativistic theory must fit galaxies, clusters, lensing, the cosmic microwave background, nonlinear structure, gravitational waves, and precision local tests without restoring a dominant unseen component under another name. At the evidence cutoff of 2026-08-20, constructive models and adverse cross-scale results coexist, while the newest Gaia wide-binary analyses directly disagree. The question remains open and the evidence contested.

Helpful background. Low-Acceleration Modified Dynamics derives the scaling law, interpolation frameworks, and requirements on relativistic completion. This record tests the dated claim that a complete theory can replace particle dark matter across regimes.

Replacement requires one predictive relativistic theory

The finite proposition is whether one causal, stable, covariant theory with fixed matter content and initial conditions predicts galaxy regularities while also fitting cluster dynamics and lensing, the CMB, linear and nonlinear structure, gravitational-wave propagation, and local tests. A rotation-curve interpolation law is a phenomenological limit, not yet a cosmology or initial-value problem.

The assessment turns on fitted versus out-of-sample galaxy predictions; dynamical versus lensing potentials; stellar mass-to-light and feedback priors; cluster hydrostatic bias and residual mass; any hot, sterile, or otherwise unseen component; the external-field effect; relativistic modes and tensor speed; cosmological initial conditions; and theoretical health.

Assessment at 2026-08-20	Meaning
Question status	Open: no single theory has completed the stated all-regime predictive test
Evidence status	Contested: strong galaxy phenomenology and viable constructions coexist with cluster, nonlinear-cosmology, and some wide-binary adverse evidence
Confidence	Moderate; high that complete replacement is unestablished, lower on the outcome of model-sensitive direct discriminants
Domain	MOND-like low-acceleration phenomenology, selected scalar–vector–tensor completions, cluster applications, νHDM cosmology, and Gaia DR3 wide binaries
What could change the conclusion	Peer review or revision of the conflicting wide-binary result, an independent Gaia-successor analysis, or one theory passing cluster, cosmological, and compact-object tests

Entry project: measure nuisance dependence in a galaxy fit

This is a practical entry for a student interested in galaxy dynamics and statistical model comparison. Preparation includes rotation curves, stellar mass-to-light ratios, distance and inclination effects, and correlated errors. A fit to one public galaxy can run on a laptop. Testing a covariant cosmology, cluster population, or wide-binary survey requires distinct data and methods.

Use the SPARC team, public database, mass-model files and data descriptions, beginning with one galaxy whose inclination and rotation-curve quality are documented. Read Lelli, McGaugh, and Schombert 2016, §3.3 to identify what each gas, disk, and bulge contribution means and which normalization has already been assumed. Then select one explicit interpolation prescription from Famaey and McGaugh 2012, §§3–4. Reconstruct the prediction in acceleration variables before fitting a free parameter.

Deliver the rotation-curve fit and a sensitivity comparison in which distance, inclination, and stellar mass-to-light ratio are varied under stated priors. Keep the chosen interpolation law and acceleration scale fixed when asking how much nuisance choices move the prediction. A one-galaxy fit is a training exercise; it neither demonstrates a universal law nor tests the relativistic lensing and cosmological sectors.

A candidate extension, with novelty unchecked, is a preselected set of galaxies used to test whether one nuisance prescription predicts a held-out subset without retuning. Define the selection before seeing residuals and preserve any environmental assumptions. Stop if noncircular motions or inclination uncertainty invalidate the simple rotation model, if the chosen law omits a relevant external-field effect, or if the conclusion comes from unconstrained nuisance parameters. Pivot to a data-quality or identifiability study. Read the cluster and cosmological counterevidence below before describing local fit success as a replacement for dark matter.

What galaxy success does and does not prove

The empirical case begins with galaxy rotation curves and acceleration relations. Across diverse surface brightness and baryonic distributions, a characteristic low-acceleration response captures nontrivial regularities. Famaey and McGaugh synthesize the galaxy phenomenology, cluster problem, relativistic theories, and cosmology in §§3–7 2012, §§3–7. The review is now old for current data, but it remains a clear statement of the successful phenomenological domain and the obstacles to completion.

Covariant completion is possible in principle. Skordis and Złośnik construct a scalar–vector–tensor theory with a MOND-like quasistatic limit and a background and linear perturbation sector resembling ΛCDM; the action, limit, and example spectra are given in the main text and Figs. 1–2 2021, action through Figs. 1–2. This is a constructive existence result, not a full precision likelihood or nonlinear validation.

Clusters remain a sharp adverse regime. An analysis of five X-COP clusters finds that Milgromian dynamics still requires centrally concentrated additional mass, although less than Newtonian inference would require; the Bayesian profiles and dependence on hydrostatic bias and external field appear in §§2–6 Kelleher and Lelli 2024, §§2–6. Candidate unseen baryons are possible, but not yet a demonstrated replacement for the missing component.

Nonlinear cosmology supplies an independent stress test. Russell et al. evolve four large collisionless simulations, including a νHDM realization designed to retain MOND galaxies and CMB behavior. In the tested implementation, structure and peculiar velocities are overproduced; the models, controls, and results are in §§2–6 Russell et al. 2026, §§2–6. It is a failure of one concrete realization, not a theorem about every covariant theory.

Results and open questions at 2026-08-20

Claim or evidence	What it supports	What it does not establish
Galaxy acceleration regularities	A compact and predictive low-acceleration phenomenology	A relativistic cosmology or absence of unseen matter
Scalar–vector–tensor construction	Existence of a covariant model matching selected galaxy and linear-cosmology behavior	Nonlinear structure, clusters, precision likelihoods, or unique parameter selection
X-COP cluster profiles	Residual central missing mass under stated Milgromian and hydrostatic assumptions	Universal failure of every relativistic completion
νHDM simulations with controls	Severe nonlinear structure and velocity failure in one concrete cosmology	A class-wide no-go theorem
Conflicting Gaia DR3 wide-binary analyses	Direct low-acceleration sensitivity and consequential analysis dependence	A settled Newtonian or MOND verdict

The galaxy row carries real explanatory weight, but an all-dark-matter replacement claim is conjunctive: failing a necessary cluster or cosmological row cannot be compensated by counting more galaxy fits. Conversely, adverse results for selected theories do not erase the empirical regularities that motivated them.

Why the wide-binary verdict is not settled

Wide binaries sample accelerations near the proposed transition using local stellar systems, but projected velocities, orbital populations, astrometric quality, unresolved triples, and sample selection are decisive. Cookson et al. apply stringent Gaia DR3 quality cuts and a multiple-star model and find no MOND-like boost 2026, §§2–7. Their result is peer reviewed in MNRAS 547, stag342.

A later submitted preprint by Chae and Yoon argues that alternative calibration and selection recover a low-acceleration anomaly 2026, §§2–7. The shared Gaia data make this a methodological conflict rather than independent replication. A third updated mixture analysis, including realistic triples, prefers Newtonian dynamics but reports reduced preference relative to its first version and emphasizes hidden-companion modeling Pittordis, Sutherland, and Shepherd 2025, §§2–6. These opposing conclusions justify contested, not selective citation of one result.

Counterexamples, null results, and failed routes

Cluster residual mass is a counterexample to the claim that the galaxy-scale law automatically eliminates unseen matter at larger scale. The νHDM simulation is a counterexample to the inference that matching the CMB and galaxy limit guarantees acceptable nonlinear structure. A locally screened or luminal tensor sector must also be demonstrated; it cannot be assumed from the nonrelativistic law.

The failed route on the other side is to declare modified dynamics ruled out from a single wide-binary sample or one cosmological implementation. Shared Gaia data and disputed companion calibration prevent a decisive local verdict, and theory space is broader than νHDM. The evidence rejects a demonstrated all-regime replacement, not the existence of low-acceleration phenomena or every possible completion.

What would change the assessment

A positive shift would require one preregistered relativistic model—parameters and matter content fixed before the comparison—to predict galaxy, cluster, lensing, CMB, nonlinear structure, gravitational-wave, and compact-object observables through public likelihoods. A negative shift could follow from a theory-class obstruction or from independent, selection-controlled low-acceleration tests that repeatedly exclude the predicted external-field and velocity distributions. Peer review or a material revision of the Chae–Yoon result, and a Gaia-successor analysis with public query and likelihood, are immediate triggers.

Research checklist

• State the covariant action, matter content, initial conditions, and relation to the nonrelativistic interpolation law.
• Separate fitted galaxy quantities from predictions made before seeing the target sample.
• Propagate the same lensing and dynamical potentials through galaxies and clusters.
• Pin stellar mass-to-light, gas, hydrostatic-bias, external-field, and distance priors.
• For wide binaries, publish the Gaia query, astrometric cuts, orbit and triple population, and projection likelihood.
• For cosmology, pin transfer functions, simulation code, resolution, box, baryonic prescription, and matched ΛCDM controls.
• Check relativistic modes, tensor speed, stability, causality, and the initial-value problem.
• Report which required unseen components remain and whether they dominate the mass budget.

Source and data map

Famaey and McGaugh supply the broad phenomenological synthesis. Skordis and Złośnik provide the constructive covariant example. Kelleher and Lelli test cluster residual mass; Russell et al. supply the current nonlinear νHDM adverse simulation. Cookson et al., Chae and Yoon, and Pittordis et al. form a deliberately paired wide-binary evidence set with their current publication and version status.

No end-to-end rerun was performed. SPARC, X-COP, Gaia, and simulation products have different selections and no verified joint public likelihood under one theory. Reproduction must pin the action and matter content, interpolation and external-field prescription, galaxy and cluster nuisance models, Gaia query and hidden-multiple model, cosmological initial conditions, code revision and convergence, CMB and structure likelihoods, and relativistic constraints. Paper availability does not establish software-level reproducibility; durable environments for the 2026 wide-binary and νHDM analyses were not verified.

References

• Chae, K.-H., and Yoon, J. 2026, “Revisiting Data Quality Control and Multiple-Star Modeling in Wide Binary Gravity Tests: Confirmation of MOND-Type Gravitational Anomaly at Low Acceleration,” arXiv:2607.14450v1, submitted preprint, open preprint.
• Cookson, S. A., Banik, I., El-Badry, K., Sutherland, W., Penoyre, Z., Pittordis, C., and Clarke, C. J. 2026, “A Quality Framework for Testing Gravity with Wide Binaries: No Evidence for MOND,” Monthly Notices of the Royal Astronomical Society 547, stag342, DOI 10.1093/mnras/stag342.
• Famaey, B., and McGaugh, S. S. 2012, “Modified Newtonian Dynamics (MOND): Observational Phenomenology and Relativistic Extensions,” Living Reviews in Relativity 15, 10, DOI 10.12942/lrr-2012-10.
• Kelleher, R., and Lelli, F. 2024, “Galaxy Clusters in Milgromian Dynamics: Missing Matter, Hydrostatic Bias, and the External Field Effect,” arXiv:2405.08557v2, accepted in Astronomy & Astrophysics, open preprint.
• Lelli, F., McGaugh, S. S., and Schombert, J. M. 2016, “SPARC: Mass Models for 175 Disk Galaxies with Spitzer Photometry and Accurate Rotation Curves,” Astronomical Journal 152, 157, DOI; open preprint.
• Pittordis, C., Sutherland, W., and Shepherd, P. 2025, “Wide Binaries from Gaia DR3: Testing GR vs MOND with Realistic Triple Modelling,” Open Journal of Astrophysics 8, DOI 10.33232/001c.142887.
• Russell, A., Banik, I., Cray, O., and Zhao, H. 2026, “How Does a MOND Cosmology Fare on Gpc Scales?—Collisionless N-Body Simulations of νHDM,” Monthly Notices of the Royal Astronomical Society 547, stag399, DOI 10.1093/mnras/stag399.
• Skordis, C., and Złośnik, T. 2021, “New Relativistic Theory for Modified Newtonian Dynamics,” Physical Review Letters 127, 161302, DOI 10.1103/PhysRevLett.127.161302.
• SPARC team. “Spitzer Photometry and Accurate Rotation Curves.” Public rotation-curve and mass-model database. Official database.