Modified Newtonian Dynamics (MOND)  

In General > s.a. variation of constants.
* Idea: At accelerations below a certain value a0 (g = ∇Φ < a0), Newton's second law of dynamics is replaced by F = ma2/a0.
* History: 1983, Proposed by Milgrom as a way to explain flat galactic rotation curves without the need for dark matter; To explain the flatness of the curves, one can set a0 ~ 1.2 × 10−10 m/s2 ~ cH0/6; The effective gravitational attraction approaches (gN a0)1/2, where gN is the usual Newtonian acceleration; The effective force goes like 1/r at large distances.
* Consequences: When a = (gN a0)1/2 ("deep MOND"), a body gravitationally bound to a mass M will orbit with speed v4 = a0GM, independent of distance! (The exponent agrees with the Tully-Fisher relation); If used as alternative to dark matter (but possibly with a cosmological constant), the theory predicts the ratio between the heights of the peaks of the cmb power spectrum; 2004, A1 / A2 agrees with WMAP data, A2 / A3 has not been reliably measured yet.
* Status: 2004, It is a phenomenological proposal, possibly related to a modification of Newton's law of motion F = ma or of the Poisson equation for gravity, but is still lacking a theoretical interpretation and covariant formulation; 2004, Proposal of TeVeS by Bekenstein; 2007, University of Washington measurements support the validity of Newton's second law down to 5 × 10−14 m/s2; 2018, More lack of evidence of a fundamental acceleration in galaxies.
@ Reviews: Milgrom APPB(01)ap-ln, a0801-conf; Sanders MPLA(03); Scarpa AIP(06)ap; Frank disc(06)aug [I]; Bekenstein CP(06)ap/07; Milgrom a0908 [semi-popular], AIP(10)-a0912; Dodelson IJMPD(11)-a1112-GRF, comment Moffat & Toth a1112 [challenges]; Famaey & McGaugh LRR(12)-a1112; Famaey & McGaugh a1310-conf [phenomenology]; Sanders CJP(14)-a1404 [historical perspective]; Milgrom CJP(15)-a1404; Bugg CJP(14)-a1405 [critical appraisal]; Sanders 16 [and concordance cosmology]; Merritt 20 [philosophical].
@ General papers: Milgrom ApJ(83), ApJ(83); Milgrom PLA(99)ap/98 [as vacuum effect], NAR(02)ap [rev]; Sanders ap/01-conf; Soussa & Woodard CQG(03)ap, Soussa ht/03-proc [non-local formulation]; Darabi IJTP(10)-a0908 [Machian interpretation]; Milgrom MNRAS(10)-a0911 [quasi-linear formulation]; Bugg CJP(13)-a1304 [novel interpretation]; Milgrom PRD(15)-a1507 [new perspective], SHPMP(20)-a1910-conf [vs dark matter].
@ Relativistic: Demir & Karahan EPJC(14)-a1408; Barrientos & Mendoza EPJP(16)-a1602; Sussman & Hernández a1908 [and cosmic expansion rate].
@ From modified inertia: Milgrom EAS(06)ap/05-proc [modified inertia vs modified gravity]; Wang a1011; Milgrom APPB(11)-a1111-conf; Namouni MNRAS-a1504; Costa et al a1904 [local Lagrangian].
@ As weak-field limit of extended metric theories: Bernal et al EPJC(11)-a1108, Mendoza et al AIP(12)-a1202; Barrientos & Mendoza PRD(18)-a1808.
@ Other origin: Jordan ap/04 [acceleration fluctuations]; Kao ap/06 [extra dimension]; Blanchet CQG(07)ap/06 [gravitational polarization]; Zaveri PiP-a0805; Zhao a0805 [neutrino-gravity coupling]; Milgrom ApJ(09)-a0810 [and spacetime scale invariance]; Pikhitsa a1010 [from gravitational thermodynamics]; Sebastian & Kuriakose a1104 [boundary terms in the gravitational Hamiltonian]; Bernal et al MPLA(11)-a1110 [acceleration scale as fundamental quantity]; Trippe JKAS(13)-a1303 [from massive gravitons]; Carranza & Mendoza JModP(15)-a1402 [as an entropic force]; Schiffer a1403 [cosmological expansion?]; Milgrom a1804-in [from a brane-world picture]; Giusti a2002, Varieschi a2003 [based on fractional calculus formalism]; > s.a. entropic gravity.
@ Other applications: McLaughlin & Meylan ap/03-in [MOND not needed]; Ciotti & Binney MNRAS(04)ap [two-body relaxation].
@ Other consequences: Ignatiev PRL(07)gq/06 + news pw(07)mar [possible violation of Newton's second law – SHLEM]; Shariati & Jafari a0710 [and conservation of energy]; Ignatiev PRD(08)-a0802 [test using high-latitude effect on Earth]; > s.a. black holes.
@ Alternatives: Romero & Zamora PRD(06)ap; Blanchet et Combes Rech-a0910 [dipolar matter]; Rastall CJP(14)-a1401 [theory with two separate forces].
> Online resources: see the MOND Pages; Wikipedia page.

And Gravitation > s.a. MOND and astrophysics / cosmology; jacobi dynamics; Mimetic Gravity; MOG; TeVeS; theories of gravitation.
* AQUAL: An implementation of MOND as a non-relativistic modified-gravity theory.
* External field effect: In MOND, the internal dynamics of a gravitating system s embedded in a larger one S is affected by the external background field of S even if it is constant and uniform, thus implying a violation of the Strong Equivalence Principle.
@ General references: Mendes & Opher PLB(01)ap [sub-mm tests]; Roscoe GRG(04); Bekenstein PRD(04)ap; Sanders LNP(07)ap/06; Bruneton & Esposito-Farèse PRD(07)-a0705; Bekenstein NPA(09)-a0901 [rev, AQUAL], in(10)-a1001 [rev]; Zhao et al PRD(10)-a1007; Skordis & Zlosnik PRD(12)-a1101 [geometry]; Fazy PRD(13)-a1302 [MOND as quantum-statistical modified entropic gravity]; Smolin PRD(17)-a1704 [as a regime of quantum gravity].
@ Bimetric MOND gravity: Milgrom PRD(09)-a0912; Milgrom MNRAS(10)-a1001 [and twin matter]; Clifton & Zlosnik PRD(10)-a1002 [FLRW cosmology]; Milgrom PRD(10)-a1006 [growth of perturbations]; Milgrom PRD(14)-a1308 [gravitational waves]; Milgrom a1310-conf [rev].
@ Other theories: Kao gq/05 [and induced gravity]; Zlosnik et al PRD(06)gq [vector-tensor theory]; Falcon a1007 [and FLRW cosmology]; Woodard CJP(14)-a1403 [MOND as non-local residual effect from the vacuum polarization of infrared gravitons]; Barrientos & Mendoza EPJP(17)-a1612 [as the weak-field limit of a theory with torsion]; Christodoulou & Kazanas a1901 [as low-acceleration limit of G(a) gravity]; Skordis & Złosnik a2007; Barrientos et al a2008 [with curvature-matter couplings]; > s.a. hořava gravity.
@ Solutions, special systems: Giannios PRD(05) [spherical static solutions]; Malekjani et al ApJ(09)-a0811 [spherical collapse].
@ Proposed tests: Gundlach et al PRL(07) + pw(07)apr [lab test]; De Lorenci et al A&A(09)-a1002 [small-acceleration test]; Trenkel et al a1001 [LISA]; Magueijo & Mozaffari PRD(12)-a1107 [LISA Pathfinder]; Das & Patitsas PRD(13)-a1305 [in freely-falling laboratories]; > s.a. equivalence principle.
@ Other phenomenology: Zhao & Famaey PRD(10) [virial theorem and elliptical shells]; Milgrom PRL(11) [and gravitational Cerenkov losses]; Milgrom MNRAS(12)-a1205 [in isolated high-acceleration systems]; Golovnev & Masalaeva GRG(14)-a1306 [gravitational collapse]; Milgrom PRD(14)-a1311 [virial theorem in general theories]; Blanchet & Bernard IJMPcs(14)-a1403 [and gravitational polarization]; Chesler & Loeb PRL(17)-a1704 [fatal inconsistencies of two relativistic generalizations with gravitational-wave observations]; Klein CQG(20)-a1901 [evidence from Cavendish-type experiments].

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