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MOND is an example of a class of theories known as [[modified models of gravity|modified gravity]], and is an alternative to the hypothesis that the dynamics of galaxies are determined by massive, invisible [[dark matter halo]]s. Since Milgrom's original proposal, proponents of MOND have claimed to successfully predict a variety of galactic phenomena that they state are difficult to understand as consequences of dark matter.<ref name="tale of two paradigms">{{Cite journal |last = McGaugh |first = S. |title = A Tale of Two Paradigms: the Mutual Incommensurability of LCDM and MOND |date=2015 |arxiv = 1404.7525 |bibcode = 2015CaJPh..93..250M |doi = 10.1139/cjp-2014-0203 |volume=93 |issue = 2 |journal=Canadian Journal of Physics |pages=250–259| s2cid = 51822163 }}</ref><ref>{{cite journal |author=Kroupa, P. |author2=Pawlowski, M. |author3=Milgrom, M. |year=2012 |title=The failures of the standard model of cosmology require a new paradigm |journal=International Journal of Modern Physics |volume=21 |issue=14 |page= 1230003 |doi=10.1142/S0218271812300030|arxiv=1301.3907 |bibcode= 2012IJMPD..2130003K|s2cid=118461811 }}</ref>
Although MOND explains the anomalously high rotational velocities of galaxies at their edges by the [[Tully-Fisher relation]]ship, it does not fully explain the velocity dispersion of individual galaxies within galaxy clusters.<ref
In 2017, the precise measurement of the speed of gravitational waves relative to the speed of light ruled out a certain class of modified gravity theories, but concluded that other MOND theories that do not require dark matter remain viable.<ref name="Boran">{{cite journal |last1=Oran |first1=Sibel |last2=Desai |first2=Santana |last3=Kaya |first3=Emre |last4=Woodard |first4=Richard |year=2018 |title=GW170817 Falsifies Dark Matter Emulators |journal=Physical Review D |volume=97 |issue=4 |pages=041501 |arxiv=1710.06168 |doi=10.1103/PhysRevD.97.041501 |bibcode=2018PhRvD..97d1501B |s2cid=119468128}}</ref> Two years later, theories put forth by Constantinos Skordis and Tom Zlosnik were consistent with gravitational waves that always travel at the speed of light. Later still in 2021, Skordis and Zlosnik developed a subclass of their theory called "RMOND", for "relativistic MOND", which had "been shown to reproduce in great detail the main observations in cosmology, including the cosmic-microwave-background power spectrum, and the matter structure power spectrum."<ref name="Milgrom Scholarpedia"/><ref name=RMOND>{{cite journal |title=New Relativistic Theory for Modified Newtonian Dynamics |author=Constantinos Skordis |author2=Tom Złośnik |name-list-style=amp |date=2021 |journal=Physical Review Letters |volume=127 |issue=16 |pages=161302 |doi=10.1103/PhysRevLett.127.161302 |pmid=34723619 |bibcode=2021PhRvL.127p1302S|arxiv = 2007.00082 |s2cid=220281053}}</ref>
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=== Outstanding problems for MOND ===
The most serious problem facing Milgrom's law is that it cannot eliminate the need for dark matter in all astrophysical systems: galaxy clusters show a residual mass discrepancy even when analyzed using MOND.<ref name="Hodson2017"/><ref name = "tale of two paradigms"/> The fact that some form of unseen mass must exist in these systems detracts from the adequacy of MOND as a solution to the missing mass problem, although the amount of extra mass required is a fifth that of a Newtonian analysis, and there is no requirement that the missing mass be non-baryonic. It has been speculated that 2 eV neutrinos could account for the cluster observations in MOND while preserving the hypothesis's successes at the galaxy scale.<ref>{{Cite journal |last1=Angus |first1=Garry W. |last2=Shan |first2=Huan Yuan |last3=Zhao |first3=Hong Sheng |last4=Famaey |first4=Benoit |name-list-style=amp |date=2007 |title=On the Proof of Dark Matter, the Law of Gravity, and the Mass of Neutrinos |journal=The Astrophysical Journal Letters |volume=654 |issue=1 |pages=L13–L16 |doi=10.1086/510738 |arxiv=astro-ph/0609125 |bibcode=2007ApJ...654L..13A|s2cid=17977472 }}</ref><ref>{{Cite journal|author=R.H. Sanders|date=2007|title=Neutrinos as cluster dark matter|journal=[[Monthly Notices of the Royal Astronomical Society]]|arxiv=astro-ph/0703590 |bibcode = 2007MNRAS.380..331S |doi = 10.1111/j.1365-2966.2007.12073.x|volume=380|issue=1|pages=331–338 |s2cid=14237211}}</ref> Indeed, analysis of sharp lensing data for the galaxy cluster Abell 1689 shows that MOND only becomes distinctive at Mpc distance from the center, so that Zwicky's conundrum remains,<ref>{{Cite journal|title=How Zwicky already ruled out modified gravity theories without dark matter|first=Theodorus M.|last=Nieuwenhuizen |journal=Fortschritte der Physik|volume=65|issue=6–8|page=1600050 |doi=10.1002/prop.201600050|arxiv=1610.01543|date=2016 |s2cid=118676940}}</ref> and 1.8 eV neutrinos are needed in clusters.<ref>{{Cite journal|title=Dirac neutrino mass from a neutrino dark matter model for the galaxy cluster Abell 1689|first=Theodorus M.|last=Nieuwenhuizen |journal=Journal of Physics: Conference Series|volume=701|issue=1|page=012022(13pp)|date=2015 |doi=10.1088/1742-6596/701/1/012022|arxiv=1510.06958|bibcode=2016JPhCS.701a2022N |s2cid=3599969}}</ref>
The 2006 observation of a pair of colliding galaxy clusters known as the "[[Bullet Cluster]]",<ref>{{Cite journal |last1=Clowe |first1=Douglas |last2=Bradač |first2=Maruša |last3=Gonzalez |first3=Anthony H. |last4=Markevitch |first4=Maxim |last5=Randall |first5=Scott W. |last6=Jones |first6=Christine |last7=Zaritsky |first7=Dennis |name-list-style=amp |date=2006 |title=A Direct Empirical Proof of the Existence of Dark Matter |journal=The Astrophysical Journal Letters |volume=648 |issue=2 |pages=L109–L113 |doi=10.1086/508162 |arxiv=astro-ph/0608407 |bibcode=2006ApJ...648L.109C|s2cid=2897407 }}</ref> poses a significant challenge for all theories proposing a modified gravity solution to the missing mass problem, including MOND. Astronomers measured the distribution of stellar and gas mass in the clusters using [[visible light|visible]] and [[X-ray]] light, respectively, and in addition mapped the inferred dark matter density using gravitational lensing. In MOND, one would expect the "missing mass" to be centred on regions of visible mass which experience accelerations lower than a<sub>0</sub> (assuming the external field effect is negligible). In ΛCDM, on the other hand, one would expect the dark matter to be significantly offset from the visible mass because the halos of the two colliding clusters would pass through each other (assuming, as is conventional, that dark matter is collisionless), whilst the cluster gas would interact and end up at the centre. An offset is clearly seen in the observations. It has been suggested, however, that MOND-based models may be able to generate such an offset in strongly non-spherically symmetric systems, such as the Bullet Cluster.<ref>{{cite journal| author=G.W. Angus |author2=B. Famaey |author3=H. Zhao |name-list-style=amp | title=Can MOND take a bullet? Analytical comparisons of three versions of MOND beyond spherical symmetry| journal=Mon. Not. R. Astron. Soc.| volume=371| issue=1| pages=138–146 |date=September 2006| doi= 10.1111/j.1365-2966.2006.10668.x| arxiv=astro-ph/0606216v1|bibcode = 2006MNRAS.371..138A |s2cid=15025801 }}</ref>
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