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The standard model of cosmology including dark energy and dark matter is in very good agreement with observation on scales above those of galaxies, but in its standard version becomes problematic below this scale (there are variants that address this, such as fuzzy dark matter).

Curiously though, the particular behaviour of experimental data on these “small” cosmological scales turns out to have a remarkably simple and universal phenomenological fit by a simple modification of the force law of Newtonian mechanics (“Newton’s third law”, corrections from general relativity are typically very small for the effects in question).

MOND is the abbreviation for this modified Newtonian dynamics (Milgrom 83 a, Milgrom 83 b, Milgrom 83 c). This refers to the proposal of modifying Newton’s third law

F=ma F = m a

relating the force experienced by a body of mass mm to its acceleration aa by an expression of the form

F=mμ(a/a 0)a F = m \,\mu(a/a_0)\, a

for some acceleration scale a 0a_0 and some interpolating function μ:\mu \colon \mathbb{R} \to \mathbb{R}.

The motivation is that choosing the constant a 0a_0 and the function μ\mu suitably, then such a modified formula fits the rotation-velocities of observed galaxies in dependence of the radius remarkably well, something which the standard model of cosmology with dark matter still has some problems with (but see Kaplinghat-Turner 02, BLSF 09, Chan 13).

In 2020, David Merritt wrote a review of MOND and dark matter which stated that the observational evidence favors MOND over dark matter (Merritt20).

Relativistic extensions of MOND

The original MOND model by Milgrom is an ad-hoc such modification of the basic laws of physics and breaks many established properties of physics, such as the principle of equivalence in general relativity and various conservation laws. Thus, many theories have been developed to reconcile MOND with relativity, including:

In addition, there are also studies of relativistic MOND gravity in general (TMZ23, THCZ23).

These theories tend to postulate new relativistic fields adjoined to plain Einstein gravity. While the relativistic interactions of these hypothetical new fields is designed to mimic the originally postulated MOdfied Newtonian Dynamics in appropriate regime, to be phenomenologically viable they must otherwise be effectively unobservable and as such are rather like the dark matter fields whose introduction the original idea of MOND it was to avoid. Therefore, the difference between the oxymoronic “relativistic MOND” and mainstream dark matter is now more one of style and focus than of principle.

Tensor-Vector-Scalar gravity

The first such proposal for such a theory apart from gravity+dark matter itself (Kaplinghat-Turner 02, BLSF 09, Chan 13) is to add to Einstein gravity a unit vector field and a scalar field (Bekenstein 04, “TeVeS”), themselves thus otherwise unobserved “dark fields”, as it were, but, as opposed to say the axion dark matter candidate, not motivated beyond the desire to fit galaxy rotation curves.

From Bekenstein 04, p. 9 one sees explicitly that TeVeS is just Einstein-gravity coupled to peculiar “matter” fields:

  • An alternative proposal is that of fuzzy dark matter, where the theory of gravity is left as is, but one assumes that there is dark matter which is so extremely light that its de Broglie wavelength is of the scales of galaxies. Such fuzzy dark matter models make the same prediction as cold dark matter on cosmological scales, but change behaviour on scales of galaxies due to the quantum nature of these light particles becoming relevant here. This change of behaviour has been argued to account for the kind of effects that MOND is a fit for.


Original articles

The concept of MOND is due to

  • Mordehai Milgrom, A modification of the Newtonian dynamics as a possible alternative to the hidden mass hypothesis, Astrophysical Journal. 270: 365–370. (1983) doi:10.1086/161130.

  • Mordehai Milgrom, A modification of the Newtonian dynamics - Implications for galaxies, Astrophysical Journal. 270: 371–389. (1983) doi:10.1086/161131.

  • Mordehai Milgrom, A modification of the Newtonian dynamics - Implications for galaxy systems, Astrophysical Journal. 270: 384. (1983) doi:10.1086/161132

There are many relativistic extensions of MOND, which are listed in the following section:

Relativistic MOND models

On relativistic MOND models:


General review includes

Experimental constraints

The stark failure of plain MOND to fit data on large cosmological scales is highlighted in

  • Scott Dodelson, The Real Problem with MOND, Int. J. Mod. Phys. D, 20, 2749 (2011). (arXiv:1112.1320)

  • Kris Pardo, David Spergel, What is the price of abandoning dark matter? Cosmological constraints on alternative gravity theories (arXiv:2007.00555)

The instability of its relativistic completion by TeVeS was pointed out in

  • Michael D. Seifert, Stability of spherically symmetric solutions in modified theories of gravity, Phys.Rev.D76:064002, 2007 (arXiv:gr-qc/0703060)

The detection of gravitational waves coincident with electromagnetic radiation from merging neutron stars (event GW170817, LIGO-Virgo 17) constrains relativistic completions of MOND:

  • Jose María Ezquiaga, Miguel Zumalacárregui, Dark Energy after GW170817 (arXiv:1710.05901)

  • Sibel Boran, Shantanu Desai, Emre Kahya, Richard Woodard, GW170817 Falsifies Dark Matter Emulators (arXiv:1710.06168)

The observation of a galaxy that does not exhibit the effect which MOND claims is universal (otherwise attributed to the presence of dark matter) is reported in

Regardless of the formation history of NGC1052–DF2, its existence has implications for the dark matter paradigm. Our results demonstrate that dark matter is separable from galaxies, which is (under certain circumstances) expected if it is bound to baryons through nothing but gravity. The “bullet cluster” demonstrates that dark matter does not always trace the bulk of the baryonic mass, which in clusters is in the form of gas. NGC1052–DF2 enables us to make the complementary point that dark matter does not always coincide with galaxies either: it is a distinct “substance” that may or may not be present in a galaxy. Furthermore, and paradoxically, the existence of NGC1052–DF2 may falsify alternatives to dark matter. In theories such as MOND and the recently proposed emergent gravity paradigm a “dark matter” signature should always be detected, as it is an unavoidable consequence of the presence of ordinary matter. In fact, it had been argued previously that the apparent absence of galaxies such as NGC1052–DF2 constituted a falsification of the standard cosmological model, and evidence for modified gravity.

The observation that wide binaries do not seem to have MOND effects:

The observation that SPARC galaxies prefer dark matter over MOND:

MOND phenomenology from actual dark matter

Derivations of the MOND phenomenology from actual dark matter is discussed in the following articles:

  • Manoj Kaplinghat, Michael S. Turner, How Cold Dark Matter Theory Explains Milgrom’s Law, Astrophys.J. 569 (2002) L19 (arXiv:astro-ph/0107284)

  • Jean-Philippe Bruneton, Stefano Liberati, Lorenzo Sindoni, Benoit Famaey, Reconciling MOND and dark matter?, Journal of Cosmology and Astroparticle Physics, Issue 03, pp. 021 (2009) (arXiv:0811.3143)

  • Man Ho Chan, Reconciliation of MOND and Dark Matter theory, Phys. Rev. D, 88, 103501 (2013) (arXiv:1310.6801)

and specifically for axionic fuzzy dark matter:

and for fuzzy dark matter with superfluid-effects includes in

Hybrid MOND dark matter models

Hybrid models which contain both MOND and dark matter are explored in

Other references

For possible MOND effects in the Solar System:

  • Cezary Migaszewski, On the origin of extreme trans-Neptunian objects within Modified Newtonian Dynamics (arXiv:2303.13339)

MOND as an alternative to Planet Nine hypothesis:

  • Katherine Jones-Smith, Harsh Mathur, Modified Newtonian Dynamics as an Alternative to the Planet Nine Hypothesis (arXiv:2304.00576)

Last revised on April 10, 2024 at 04:11:26. See the history of this page for a list of all contributions to it.