Living Reviews in Relativity

"Modified Newtonian Dynamics (MOND):
Observational Phenomenology and Relativistic Extensions"
by
Benoît Famaey and Stacy S. McGaugh 

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Abstract
1 Introduction
2 The Missing Mass Problem in a Nutshell
3 A Brief Overview of the ΛCDM Cosmological Model
3.1 Dark Energy (Λ)
3.2 Cold Dark Matter (CDM)
4 Some Challenges for the ΛCDM Model
4.1 Coincidences
4.2 Unobserved predictions
4.3 Unpredicted observations
5 Milgrom’s Empirical Law and “Kepler Laws” of Galactic Dynamics
5.1 Milgrom’s law and the dielectric analogy
5.2 Galactic Kepler-like laws of motion
6 Milgrom’s Law as a Modification of Classical Dynamics: MOND
6.1 Modified inertia or modified gravity: Non-relativistic actions
6.2 The interpolating function
6.3 The external field effect
6.4 MOND in the solar system
6.5 MOND in rotationally-supported stellar systems
6.6 MOND in pressure-supported stellar systems
7 Relativistic MOND Theories
7.1 Scalar-tensor k-essence
7.2 Stratified theory
7.3 Original Tensor-Vector-Scalar theory
7.4 Generalized Tensor-Vector-Scalar theory
7.5 Bi-Scalar-Tensor-Vector theory
7.6 Non-minimal scalar-tensor formalism
7.7 Generalized Einstein-Aether theories
7.8 Bimetric theories
7.9 Dipolar dark matter
7.10 Non-local theories and other ideas
8 Gravitational Lensing in Relativistic MOND
8.1 Strong lensing by galaxies
8.2 Weak lensing by galaxies
8.3 Strong and weak lensing by galaxy clusters
8.4 Weak lensing by large-scale structure
9 MOND and Cosmology
9.1 Expansion history
9.2 Large-scale structure and Cosmic Microwave Background
10 Summary and Discussion
11 Acknowledgements
Open References References
Footnotes
Figures
Tables