[Paper Review] Modified Newtonian Dynamics: A Review

Benoît Famaey, Stacy McGaugh|arXiv (Cornell University)|Dec 16, 2011

Cosmology and Gravitation Theories3 citations

TL;DR

This paper reviews Modified Newtonian Dynamics (MOND) as an alternative to dark matter, proposing that a single universal force law—Milgrom's law—explains mass discrepancies in galaxies by modifying Newtonian dynamics at low accelerations. The key contribution is demonstrating that MOND successfully predicts a wide range of astrophysical observations without invoking unseen matter.

ABSTRACT

A wealth of astronomical data indicate the presence of mass discrepancies in the Universe. The motions observed in a variety of classes of extragalactic systems exceed what can be explained by the mass visible in stars and gas. Either (i) there is a vast amount of unseen mass in some novel form - dark matter - or (ii) the data indicate a breakdown of our understanding of dynamics on the relevant scales, or (iii) both. Here, we first review a few outstanding challenges for the dark matter interpretation of mass discrepancies in galaxies, purely based on observations and independently of any alternative theoretical framework. We then show that many of these puzzling observations are predicted by one single relation - Milgrom's law - involving an acceleration constant (or a characteristic surface density) of the order of the square-root of the cosmological constant in natural units. This relation can at present most easily be interpreted as the effect of a single universal force law resulting from a modification of Newtonian dynamics (MOND) on galactic scales. We exhaustively review the current observational successes and problems of this alternative paradigm at all astrophysical scales, and summarize the various theoretical attempts (TeVeS, GEA, BIMOND, and others) made to effectively embed this modification of Newtonian dynamics within a relativistic theory of gravity.

Motivation & Objective

• To examine observational challenges to the dark matter hypothesis in galaxies, independent of theoretical frameworks.
• To evaluate whether Milgrom's law—a single relation involving a universal acceleration constant—can explain observed mass discrepancies.
• To assess the success and limitations of MOND across astrophysical scales.
• To review theoretical attempts to embed MOND in a relativistic theory of gravity, such as TeVeS, GEA, and BIMOND.

Proposed method

• Analysis of astronomical data from extragalactic systems showing mass discrepancies beyond visible matter.
• Application of Milgrom's law, which modifies Newtonian dynamics at low accelerations, with a characteristic acceleration scale on the order of the square root of the cosmological constant.
• Evaluation of MOND predictions against observational data across various astrophysical systems, including galaxies and clusters.
• Review of relativistic extensions of MOND, such as Tensor-Vector-Scalar (TeVeS) theory, Generalized Einstein-Aether (GEA), and BIMOND, to assess their consistency with cosmological and astrophysical constraints.
• Comparison of MOND predictions with those of the dark matter paradigm in explaining rotation curves, mass-velocity relations, and other dynamical features.

Experimental results

Research questions

• RQ1 Can Milgrom's law explain the observed mass discrepancies in galaxies without invoking dark matter?
• RQ2 How well does MOND perform in predicting dynamical features across different astrophysical scales?
• RQ3 What are the observational successes and limitations of MOND compared to the dark matter hypothesis?
• RQ4 Can a relativistic theory of gravity be constructed that consistently embeds MOND's phenomenology?
• RQ5 What are the implications of MOND for our understanding of gravity on galactic scales?

Key findings

• Milgrom's law, involving a universal acceleration constant, successfully predicts a wide range of galactic dynamics, including rotation curves and mass-velocity relations.
• The characteristic acceleration scale in Milgrom's law is on the order of the square root of the cosmological constant in natural units, suggesting a deep connection to cosmology.
• MOND explains observed mass discrepancies in galaxies without requiring unseen dark matter, offering a consistent alternative to the dark matter paradigm.
• Relativistic extensions such as TeVeS, GEA, and BIMOND provide frameworks to embed MOND in a relativistic theory, though challenges remain in fully reconciling them with cosmological observations.
• MOND's predictions are consistent with observations across various astrophysical systems, including dwarf galaxies, spiral galaxies, and galaxy clusters.
• Despite its successes, MOND still faces unresolved challenges in explaining certain large-scale cosmological phenomena, such as the cosmic microwave background anisotropies, which remain better explained by the standard cosmological model.