The discovery of dark matter in galaxies marks a turning point in astrophysics

especially because of its conceptual relevance to cosmology. After a brief introduction to the dynamics of collisionless stellar systems, a short account is given of the study of dark halos in ellipticals. Then it is shown that the dark matter contained in galaxies does not change the value of the key cosmological parameters significantly. The text continues with an outline of some modern simulations of structure formation, a vast and fast-evolving field of research that ultimately focuses on the issues that define the formation and the evolution of galaxies and on the structure of dark halos. Then, at the forefront of current research, for the nearby and present universe the potential of modern telescopes such as Gaia is briefly recalled; for the distant and early universe, a short summary is given of the role of gravitational lensing as diagnostics of dark matter for galaxies, clusters of galaxies, and structure formation. Finally, the main steps are outlined of an attempt (MOND), started in the early 1980s and still continuing with some success, which explores the possibility that the law of gravitation requires a modification on the scales of galaxies and beyond and that dark matter does not exist.

The second variant of Milgrom’s theory (T1) derives the equations of motion from a Lagrangian formulation, allowing the theory to make predictions for a very general class of systems with arbitrary shapes. A number of confirmed, novel predictions follow from T1 including the “central surface density relation” (CSDR) and a prediction about the form of the vertical force law in the Milky Way. The theory also predicts a very low rate of mergers between galaxies, a prediction that may or may not be consistent with observations. However, the theory’s predictions about the kinematics of the largest bound structures in the universe, the galaxy clusters, appear to be incorrect.

The first variant of Milgrom’s theory (T0) consists simply of his three postulates from 1983. These postulates entail a number of novel predictions, predictions that have subsequently been confirmed by observational astrophysicists. The first is the “baryonic Tully–Fisher relation” (BTFR), a unique relation between the total mass of a galaxy and its asymptotic rotation speed. An even more surprising prediction is the “radial acceleration relation” (RAR), which states that the rotation speed anywhere in a disk galaxy is determined precisely by the observed distribution of matter – but not in the way that Newton’s laws would predict. According to Lakatos’s Methodology, these, and some other, successful novel predictions imply that Milgrom’s postulates constitute a progressive departure from the dark matter hypotheses of the standard cosmological model.

In 1983, the physicist Mordehai Milgrom initiated a new research program in cosmology, called MOND (for MOdified Newtonian Dynamics), or Milgromian dynamics. In three papers, Milgrom proposed a set of postulates describing how Newton’s laws of gravity and motion should be changed in regimes of very low acceleration. Milgrom’s postulates were designed to explain the asymptotic flatness of galaxy rotation curves, without the necessity of postulating the existence of “dark matter”. Milgrom showed that a number of other, novel predictions follow from his three postulates, and proposed these predictions as tests of the theory. Milgrom also proposed a set of guiding principles for how his nascent theory should be developed toward a more complete theory of gravity and cosmology.