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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
relating the force experienced by a body of mass $m$ to its acceleration $a$ by an expression of the form
for some acceleration scale $a_0$ and some interpolating function $\mu \colon \mathbb{R} \to \mathbb{R}$.
The motivation is that choosing the constant $a_0$ and the function $\mu$ 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).
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:
Tensor-Vector-Scalar gravity (Bekenstein 04, “TeVeS”)
Aether scalar tensor theory (SkordisZlosnik21, SkordisZlosnik22, MMH23, “AeST)
Bimetric MOND (Milgrom22)
Khronometric MOND (Flanagan23)
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.
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:
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:
On relativistic MOND models:
Jacob Bekenstein, Relativistic gravitation theory for the modified Newtonian dynamics paradigm, Physical Review D 70 8 (2004) 083509, [arXiv:astro-ph/0403694, doi:10.1103/PhysRevD.70.083509]
Constantinos Skordis, Tom Zlosnik, A new relativistic theory for Modified Newtonian Dynamics. Physical Review Letters. Volume 127, Issue 16. Published 15 October 2021 (doi:10.1103/PhysRevLett.127.161302, arXiv:2007.00082)
Constantinos Skordis, Tom Zlosnik, Aether scalar tensor theory: Linear stability on Minkowski space. Physical Review D. Volume 106, Issue 10. Published 15 November 2022. (doi:10.1103/PhysRevD.106.104041, arXiv:2109.13287)
Tobias Mistele, Stacy McGaugh, Sabine Hossenfelder, Aether Scalar Tensor theory confronted with weak lensing data at small accelerations, (arXiv:2301.03499)
Mordehai Milgrom, Broader view of bimetric MOND, Physical Review D, Volume 106, Issue 8. Published 10 October 2022. (doi:10.1103/PhysRevD.106.084010, arXiv:2208.10882)
Daniel Thomas, Ali Mozaffari, Tom Zlosnik, Consistent cosmological structure formation on all scales in relativistic extensions of MOND (arXiv:2303.00038)
Eanna Flanagan, Khronometric theories of modified Newtonian dynamics (arXiv:2302.14846)
Shuxun Tian, Shaoqi Hou, Shuo Cao, Zong-Hong Zhu, Time evolution of the local gravitational parameters and gravitational wave polarizations in a relativistic MOND theory, Physical Review D, Volume 107, Issue 4. Published 24 February 2023. (doi:10.1103/PhysRevD.107.044062, arXiv:2302.13304)
Martin Bojowald, Erick I. Duque, Emergent Modified Gravity [arXiv:2404.06375]
General review includes
Benoît Famaey and Stacy S. McGaugh, Modified Newtonian Dynamics (MOND): Observational Phenomenology and Relativistic Extensions,2012, Living Reviews in Relativity, 15, 10 (arXiv:1112.3960)
Joe Silk, Gary A. Mamon, The Current Status of Galaxy Formation (arXiv:1207.3080)
Wikipedia, Modified Newtonian dynamics
Wikipedia, Tensor–vector–scalar gravity
Phillip James E. Peebles, §5.7 “Why is MOND Successful but Unpoular” of: Anomalies in Physical Cosmology [arXiv:2208.05018]
David Merritt, A Philosophical Approach to MOND: Assessing the Milgromian Research Program in Cosmology. Cambridge University Press, 2020. ISBN:978-1108492690
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
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:
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
Lasha Berezhiani, Justin Khoury, Theory of Dark Matter Superfluidity, Phys. Rev. D 92, 103510 (2015) (arXiv:1507.01019)
Justin Khoury, Another Path for the Emergence of Modified Galactic Dynamics from Dark Matter Superfluidity, Phys. Rev. D 93, 103533 (2016) (arXiv:1602.05961)
Hybrid models which contain both MOND and dark matter are explored in
Tobias Mistele, Cherenkov radiation from stars constrains hybrid MOND dark matter models. Journal of Cosmology and Astroparticle Physics, Volume 2022, November 2022 (doi:10.1088/1475-7516/2022/11/008, arXiv:2103.16954)
Tobias Mistele, A novel Cherenkov radiation constraint for hybrid MOND dark matter models, (arXiv:2208.14308)
For possible MOND effects in the Solar System:
MOND as an alternative to Planet Nine hypothesis:
Last revised on April 10, 2024 at 04:11:26. See the history of this page for a list of all contributions to it.