Modified Newtonian Dynamics (MOND): Observational Phenomenology and Relativistic Extensions

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.

164 pages, 48 figures, 2 tables, invited review for Living Reviews in Relativity

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• Discussing the first velocity dispersion profile of an ultra-diffuse galaxy in MOND
• On the fundamentality of the radial acceleration relation for late-type galaxy dynamics
• Solar System limits on gravitational dipoles
• A Test of MONDian Gravity in $\sim$300 pressure supported elliptical galaxies from the MaNGA survey
• The Kennicutt-Schmidt law and the main sequence of galaxies in Newtonian and Milgromian dynamics
• Heat capacity of Holographic screen inspires MOND theory
• Astrodynamical Space Test of Relativity using Optical Devices I (ASTROD I) - Mission Overview
• Not All Subhaloes Are Created Equal: Modelling the Diversity of Subhalo Density Profiles in TNG50
• Dynamics of Elliptical Galaxies with Planetary Nebulae in Modified Newtonian Dynamics
• Relativistic Khronon Theory in agreement with Modified Newtonian Dynamics and Large-Scale Cosmology
• Dipolar Dark Matter as an Effective Field Theory
• Consequences of the external field effect for MOND disk galaxies in galaxy clusters
• Shell galaxies as laboratories for testing MOND
• Testing the tensor-vector-scalar Theory with the latest cosmological observations
• Interposing a Varying Gravitational Constant Between Modified Newtonian Dynamics and Weak Weyl Gravity
• Dynamical History Of The Local Group In $\Lambda$CDM $\mathrm{II}$ $-$ Including External Perturbers In 3D
• Baryon-Interacting Dark Matter: heating dark matter and the emergence of galaxy scaling relations
• The solar system test for the general modified gravity theories
• Stellar Structure Equations in Extended Palatini Gravity
• MOND in galaxy groups
• Dynamics of DiskMass Survey galaxies in refracted gravity
• Modeling Nearly Spherical Pure-bulge Galaxies with a Stellar Mass-to-Light Ratio Gradient under the $\Lambda$CDM and MOND Paradigms: I. Methodology, Dynamical Stellar Mass, and Fundamental Mass Plane
• Horndeski dark matter and beyond
• Origin of the fundamental plane of elliptical galaxies in the Coma Cluster without fine-tuning
• Cosmological Dynamics of Relativistic MOND
• HI in the Outskirts of Nearby Galaxies
• Dynamics of wide binary stars: A case study for testing Newtonian dynamics in the low acceleration regime
• Dressed black holes in the new tensor-vector-scalar theory
• Gravitational potential and galaxy rotation curves in multi-fractional spacetimes
• Sedna and the cloud of comets surrounding the Solar System in Milgromian dynamics
• Testing modified gravity at large distances with the HI Nearby Galaxy Survey's rotation curves
• How Close Dark Matter Halos and MOND Are to Each Other: Three-Dimensional Tests Based on Gaia DR2
• MOND as a peculiar case of the SIV theory
• Lopsidedness of self-consistent galaxies by the external field effect of clusters
• Self-gravitating Equilibria of Non-minimally Coupled Dark Matter Halos
• Time evolution of the local gravitational parameters and gravitational wave polarizations in a relativistic MOND theory
• The underlying radial acceleration relation
• Core Fragmentation in Simplest Superfluid Dark Matter Scenario
• Mass-Velocity Dispersion Relation in HIFLUGCS Galaxy Clusters
• Modified Gravity Theories in Light of the Anomalous Velocity Dispersion of NGC1052-DF2
• Cosmology of the Galileon extension of Bekenstein's theory of relativistic Modified Newtonian Dynamics
• Mass Discrepancy-Acceleration Relation in Einstein Rings
• Effects of Lens Motion and Uneven Magnification on Image Spectra
• Can TeVeS be a viable theory of gravity?
• Phenomenology of MOND and gravitational polarization
• Galaxies with Declining Rotation Curves
• On the absence of backsplash analogues to NGC 3109 in the $\Lambda$CDM framework
• Global stability of self-gravitating disks in modified gravity
• Predictions for the sky-averaged depth of the 21cm absorption signal at high redshift in cosmologies with and without non-baryonic cold dark matter
• Multi-TeV dark matter density in the inner Milky Way halo: spectral and dynamical constraints
• Pseudo-Evolution of Galaxies in LCDM Cosmology
• Empirical Evidence of Non-Minimally Coupled Dark Matter in the Dynamics of Local Spiral Galaxies?
• Probing modified gravitational-wave propagation through tidal measurements of binary neutron star mergers
• Wide Binaries as a Modified Gravity test: prospects for detecting triple-system contamination
• The radial acceleration relation and dark baryons in MOND
• Dark Matter in Fractional Gravity I: Astrophysical Tests on Galactic Scales
• Deep-MOND polytropes
• Testing gravity with interstellar precursor missions
• Evidence for Modified Newtonian Dynamics from Cavendish-type gravitational constant experiments
• Galaxy Rotation Curves via Conformal Factors
• A test of constancy of dark matter halo surface density and radial acceleration relation in relaxed galaxy groups
• Exploring the effects of primordial non-Gaussianity at galactic scales
• Dark matter superfluid and DBI dark energy
• MOND prediction of a new giant shell in the elliptical galaxy NGC3923
• Testing Modified Dark Matter with Galaxy Clusters: Does Dark Matter know about the Cosmological Constant?
• A test of Radial Acceleration Relation for the {\it Giles et al Chandra} cluster sample
• Will-Nordtvedt PPN formalism applied to renormalization group extensions of general relativity
• Acausality in Superfluid Dark Matter and MOND-like Theories
• Stellar population synthesis models with a physically varying IMF
• Satellite Test of the Equivalence Principle as a Probe of Modified Newtonian Dynamics
• Model Independent analysis of MeV scale dark matter: II. Implications from $e^{-}{e}^{+}$ colliders and Direct Detection
• Theoretical implications of the galactic radial acceleration relation of McGaugh, Lelli, and Schombert
• Evolution of spiral galaxies in nonlocal gravity
• Acceleration Relations in the Milky Way as Differentiators of Modified Gravity Theories
• Logarithmic corrections to Newtonian gravity and Large Scale Structure
• A simple model for explaining Galaxy Rotation Curves
• Alternative gravity rotation curves for the Little Things Survey
• Cosmology in doubly coupled massive gravity: constraints from SNIa, BAO and CMB
• Lunar system constraints on the modified theories of gravity
• A Distinct Radial Acceleration Relation across Brightest Cluster Galaxies and Galaxy Clusters
• A relativistic description of MOND using the Palatini formalism in an extended metric theory of gravity
• Reconstructing a Model for Gravity at Large Distances from Dark Matter Density Profiles
• Modified Baryonic Dynamics: two-component cosmological simulations with light sterile neutrinos
• Testing emergent gravity with mass densities of galaxy clusters
• Covariant formulation of refracted gravity
• A big bounce, slow-roll inflation and dark energy from conformal gravity
• Testing Modified Gravity Theories with Numerical Solutions of the External Field Effect in Rotationally Supported Galaxies
• Constraints on Self-Interacting dark matter from relaxed galaxy groups
• The Magellanic Clouds are very rare in the IllustrisTNG simulations
• Mass-Velocity Dispersion Relation in MaNGA Brightest Cluster Galaxies
• Are Over-massive Haloes of Ultra Diffuse Galaxies Consistent with Extended MOND?
• Ultra faint dwarf galaxies: an arena for testing dark matter versus modified gravity
• Three problems of superfluid dark matter and their solution
• Enigmatic Velocity Dispersions of Ultra-Diffuse Galaxies in Light of Modified Gravity Theories and Radial Acceleration Relation
• Aether scalar tensor theory: Hamiltonian Formalism
• Disk galaxies are self-similar: the universality of the HI-to-Halo mass ratio for isolated disks
• The phenomenology of the external field effect in cold dark matter models
• Emergent Dark Matter in Late Time Universe on Holographic Screen
• The Radial Acceleration Relation and a Magnetostatic Analogy in Quasilinear MOND
• The specific frequency and the globular cluster formation efficiency in Milgromian dynamics
• Asymptotic kinematics of Globular Clusters: the emergence of a Tully-Fisher relation
• A new estimator of the deceleration parameter from galaxy rotation curves
• Galaxy rotation curve in hyperconical universes: a natural relativistic MOND
• The dynamics of three nearby E0 galaxies in refracted gravity
• What have we learned from observational cosmology ?
• The proper motion of stars in dwarf galaxies: distinguishing central density cusps from cores
• Stellar Bar evolution in the absence of dark matter halo
• Astrophysical constraints and insights on extended relativistic gravity
• Gauss's Law and the Source for Poisson's Equation in Modified Gravity with Varying G
• A Cusp-Core like challenge for Modified Newtonian Dynamics
• The MOND External Field Effect on the Dynamics of the Globular Clusters: General Considerations and Application to NGC 2419
• Towards an explanation of orbits in the extreme trans-Neptunian region: The effect of Milgromian dynamics
• MOND fiducial specific angular momentum of disc galaxies
• On the origin of extreme trans-Neptunian objects within Modified Newtonian Dynamics
• A new scale in the quasi-static limit of Aether Scalar Tensor Theory
• Imprint of the galactic acceleration scale on globular cluster systems
• Low-acceleration dwarf galaxies as tests of quantised inertia
• The Diffuse Light of the Universe - On the microwave background before and after its discovery: open questions
• Dynamics of a higher-dimension Einstein-Scalar-Gauss-Bonnet cosmology
• Quasilocal Newtonian limit of general relativity and galactic dynamics
• Testing MOND on Earth
• Distribution of star formation rates during the rapid assembly of NGC 1399 as deduced from its globular cluster system
• MIGHTEE-HI: The radial acceleration relation with resolved stellar mass measurements
• A compactness result for non-local unregularized gradient flow lines
• Probing modified Newtonian dynamics with hypervelocity stars
• Scale-invariant dynamics in the Solar System
• The formation of compact massive relic galaxies in MOND
• Dipolar dark matter simulations on galaxy scales with the RAMSES code
• A Multi-messenger view of Cosmic Dawn: Conquering the Final Frontier
• Testing the Collisionless Nature of Dark Matter with the Radial Acceleration Relation in Galaxy Clusters
• Motion of Particles in Solar and Galactic Systems by Using Neumann Boundary Condition
• Non-Gaussianity in the Cosmic Microwave Background Induced by Dipolar Dark Matter
• Clusters of galaxies in a Weyl geometric approach to gravity
• Two-body problem in theories with kinetic screening
• Explaining the formation of bulges with MOND
• Galaxy rotation curves and the deceleration parameter in weak gravity
• MOND implications for spectral line profiles of shell galaxies: shell formation history and mass-velocity scaling relations
• Broader view of bimetric MOND
• On the gravitational stability of the Maclaurin disk
• Central-surface-densities correlation in general MOND theories
• SHARP -- IX. The dense, low-mass perturbers in B1938+666 and J0946+1006: implications for cold and self-interacting dark matter
• Exact semianalytical calculation of rotation curves with Bekenstein-Milgrom nonrelativistic MOND
• Macroscopic theory of dark sector
• Parameter-free prediction of the asymptotic acceleration scale confirmed by weak lensing
• Slowly rotating black holes in the Einstein-Maxwell-scalar theory
• Dark Matter Fraction in Disk-Like Galaxies Over the Past 10 Gyr
• Modified Gravity (MOG) and its test on galaxy clusters
• A test of invariance of dark matter halo surface density using multiwavelength mock galaxy catalogues
• A Critique of Covariant Emergent Gravity
• Testing the local supervoid solution to the Hubble tension with direct distance tracers
• Neutron stars as probes of dark matter
• Type I shell galaxies as a test of gravity models
• A Modified Dynamical Model of Cosmology I. Theory
• No need for dark matter: resolved kinematics of the ultra-diffuse galaxy AGC 114905
• Scale Invariance at low accelerations (aka MOND) and the dynamical anomalies in the Universe
• Lessons from the Local Group (and beyond) on dark matter
• Stealth black holes in Aether Scalar Tensor theory
• Gas expulsion in MOND: the possible origin of diffuse globular clusters and ultra-faint dwarf galaxies
• Dwarf galaxies with central cores in modified Newtonian dynamics (MOND) gravity
• Asymmetry of the tidal tails of open star clusters in direct N-body integrations in Milgrom-law dynamics
• Can Massive Gravity Explain the Mass Discrepancy - Acceleration Relation of Disk Galaxies?
• Relativistic Localizing Processes Bespeak an Inevitable Projective Geometry of Spacetime
• The signatures of new physics, astrophysics and cosmology?
• Solar system tests and neutron stars in $f(R)$ gravity revisited
• Simulations of cluster ultra-diffuse galaxies in MOND
• Conformal Higgs model: Gauge fields can produce a 125GeV resonance
• Time delays across saddles as a test of modified gravity
• Parameterised free functions and saddle stresses in modified gravity
• Celestial mechanics in Newtonian-like gravity with variable $G$
• Saddle stresses for generic theories with a preferred acceleration scale
• Collapse of spherical overdensities in superfluid models of dark matter
• Constraining A String Gauge Field by Galaxy Rotation Curves and Perihelion Precession of Planets
• Newtonian Fractional-Dimension Gravity and Galaxies without Dark Matter
• Revisiting metric perturbations in tensor-vector-scalar theory
• Quantum Modified Gravity at Low Energy in the Ricci Flow of Quantum Spacetime
• Influence of selection criteria on the interpretation of rotational behaviour of wide-binary star systems
• Dark Coincidences: Small-Scale Solutions with Refracted Gravity and MOND
• Prospects for a local detection of dark matter with future missions to Uranus and Neptune
• One of Everything: The Breakthrough Listen Exotica Catalog
• On the problem of deformed spherical systems in Modified Newtonian Dynamics
• Buchdahl bound, photon ring, ISCO and radial acceleration in Einstein-æther theory
• Quantum Effects on Cosmic Scales as an Alternative to Dark Matter and Dark Energy
• The $\kappa$-model, a minimal model alternative to dark matter. Application to the galactic rotation problem
• Local Stability of Galactic Discs in Modified Dynamics
• Testing Refracted Gravity with kinematics of galaxy clusters
• Dynamical Symmetry Breaking and Negative Cosmological Constant
• The kinematics of star clusters undergoing gas expulsion in Newtonian and Milgromian dynamics
• MUSE-DARK III: The evolution of the radial acceleration relation at intermediate redshifts
• Application of Kaluza-Klein Theory in Modeling Compact Stars: Exploring Extra Dimensions
• Effect of the Solar dark matter wake on planets
• Observational dynamics of low-mass stellar systems
• Globular cluster orbital decay in dwarf galaxies with MOND and CDM: Impact of supernova feedback
• The radial acceleration relation at the EDGE of galaxy formation: testing its universality in low-mass dwarf galaxies
• Crossover in extended Newtonian gravity emerging from thermodynamics
• Testing Cotton gravity as dark matter substitute with weak lensing
• Modified Newtonian Dynamics (MOND) as a Modification of Newtonian Inertia
• Analogy of space-time as an elastic medium, estimation creep coefficient of space from MOND theory, gravitational lensing and via time data from the GPS effect, discussion of the results for dark matter and Einstein's field equation
• MUSE observations of dwarf galaxies and a stellar stream in the M83 group
• Distribution of Phantom Dark Matter in Dwarf Spheroidals
• Consistent cosmological structure formation on all scales in relativistic extensions of MOND
• The isolated elliptical galaxy NGC 5812 -- MOND or Dark Matter?
• Low-mass disc galaxies and the issue of stability: MOND vs dark matter
• Probing the nature of gravity in the low-acceleration limit: wide binaries of extreme separations with perspective effects
• Modified Inertia as Nonconservative Newtonian Dynamics
• Three-Body Problem in Modified Dynamics
• A Preference for Cold Dark Matter over Superfluid Dark Matter in Local Milky Way Data
• Peculiar dark matter halos inferred from gravitational lensing as a manifestation of modified gravity
• PySCo: A fast Particle-Mesh $N$-body code for modified gravity simulations in Python
• Addressing the core-cusp and diversity problem of dwarf and disk galaxies using cold collisionless DARKexp theory
• Is MOND necessarily nonlinear?
• The Atacama Cosmology Telescope: A Test of the Gravitational Force Law on Cosmological Scales Using the Kinematic Sunyaev-Zeldovich Effect
• A New Empirical Fit to Galaxy Rotation Curves
• Quantized Vortices in Superfluid Dark Matter
• A Relativistic Scalar Model for Fractional Interaction between Dark Matter and Gravity
• Formation of collisional ring galaxies in Milgromian dynamics
• NEWTON's trajectories versus MOND's trajectories
• A test of linearity of the ratio of dark matter to baryonic matter in galaxy clusters
• The intervelocity of galaxy pairs in $\Lambda$CDM -- The observed velocity peak at ~130 km/s is not unique to MOND
• Evolution of globular-cluster systems of ultra-diffuse galaxies due to dynamical friction in MOND gravity
• Dynamics of clusters of galaxies with extended $f(\chi )$ gravity
• Modified Newtonian Dynamics as an entropic force
• MONDian predictions for Newtonian M/L ratios for ultrafaint dSphs
• Tests of Modified Gravity Theories in the Solar System
• Test of conformal gravity as an alternative to dark matter from the observations of elliptical galaxies
• Searching for MOND in scalar-tensor theories of gravity
• Modelling Gaia photometry signals of dark halos
• Scaling relations of early-type galaxies in MOND
• Measuring Mass of Gas in Central Galaxies using weak lensing and satellite kinematics in MOND
• The $\kappa$-model under test of the SPARC database
• Many body gravity and the galaxy rotation curves
• On the emergence of gravity in a framework of emergent quantum mechanics
• Testing QUMOND theory with Galactic globular clusters in a weak external field
• MUSE-DARK-II: 3D morpho-kinematic modelling of lensed galaxies. Tully-Fisher relation of $z\sim 1$ star-forming galaxies
• Multidimensional representation of semantic relations between physical theories, fundamental constants and units of measurement with formal concept analysis
• Data Analysis Methods for Testing Alternative Theories of Gravity with LISA Pathfinder
• The galactic acceleration scale is imprinted on globular cluster systems of early-type galaxies of most masses and on red and blue globular cluster subpopulations
• MOND via Matrix Gravity
• Field equation of thermodynamic gravity and galactic rotational curves
• The "Graviton Picture": a Bohr Model for Gravitation on Galactic Scales?
• Disk galaxies and their dark halos as self-organized patterns
• Quadratic gravity potentials in de Sitter spacetime from Feynman diagrams
• Pattern dark matter and galaxy scaling relations
• Refracted Gravity Solutions from Small to Large Scales
• Cosmic backgrounds from the radio to the far-infrared: recent results and perspectives from cosmological and astrophysical surveys
• Central MONDian spike in spherically symmetric systems
• Dynamics of Dwarf Galaxies in Scalar-Tensor-Vector-Gravity
• Vector dark matter production during inflation in the gradient-expansion formalism
• Renzo's rule revisited: A statistical study of galaxies' baryon - dark matter coupling
• Absence of gravitational polarization mechanism in the canonical bimetric theory
• A test of MOND and Emergent Gravity with SMACS J0723.3-7327 using eROSITA observations
• Local Short-Time Acceleration induced Spectral Line Broadening and Possible Implications in Cosmology
• The Cen A galaxy group: dynamical mass and missing baryons
• Quantum Physics in Space
• Origin of the spectacular tidal shells of galaxy NGC474
• Overestimated inclinations of Milgromian disc galaxies: the case of the ultradiffuse galaxy AGC 114905
• Probing modified gravity with magnetically levitated resonators
• Milgrom's Law and Lambda's Shadow: How Massive Gravity Connects Galactic and Cosmic Dynamics
• On the Orbital Velocity of Isolated Galaxy Pairs: a test of gravity in the low acceleration regime
• Relativistic Fractional-Dimension Gravity
• Is the acceleration scale of the radial acceleration relation tracking the cosmic expansion rate?
• Is the cosmological constant an eigenvalue?
• Examining Baryonic Faber-Jackson Relation in Galaxy Groups
• Testing MOND using the dynamics of nearby stellar streams
• Point-like source solutions in modified gravity with a critical acceleration
• Galactic Scaling Rules in a Modified Dynamical Model
• Behavior of light polarization in photon-scalar interaction
• A bar stability criterion distinguishing between modified gravity and dark matter in galaxies
• Gravitational acceleration in a class of geometric sigma models
• The two-component virial theorem and the acceleration-discrepancy relation
• The MOND Depth Index and Dynamical Maturity Clock: Toward a Universal Classification of Galaxies and Star Clusters
• Merging Galaxy Clusters and the Search for New Physics of Dark Matter: A Review
• A Dynamical-Photometric Phase Space for Spiral Galaxies: Probing the Local Coupling Between Light and Gravity
• The modified Newtonian dynamics with an extra anti-dissipation term can yield the MOND model
• The tidal features of the classical Milky Way satellites: Expected in MOND but inconsistent with cold dark matter models
• Determination of the best dark matter profile for the Milky Way with Gaia DR3 using Bayesian Model Comparison
• Improved constraints on modified Newtonian gravity from Cassini radio tracking data
• Testing subhalo abundance matching with galaxy kinematics
• Anisotropic dispersion relation of ultralight Bose gases in modified Newtonian dynamics
• Bimetric MOND as a framework for variable-$G$ theories -- local systems and cosmology
• Cosmology with a Non-minimally Coupled Dark Matter Fluid I. Background Evolution
• Matter-antimatter asymmetry in a rotating universe: Dirac spinors in axisymmetric Bianchi IX cosmology
• A MOND model applied to the rotation curve of galaxies
• Distinct radial acceleration relations of galaxies and galaxy clusters supports hyperconical modified gravity
• Comparing dark matter and MOND hyphotheses from the distribution function of A, F, early-G stars in the solar neighbourhood