The currently favoured cosmological LCDM model critically depends on the mass-dominating existence of non-electromagnetically interacting dark matter particles
which are not described by the standard model of particle physics. But all terrestrial and space experiments designed to search for dark matter particles have yielded null results.
I describe and apply a hitherto largely ignored direct test for the existence of dark matter particles: the dynamical friction test. The motions of satellite galaxies, of galaxies within groups of galaxies, and the general properties of the galaxy population are in strong disagreement with dynamical friction due to the massive and spatially large dark matter halos. The negative outcome of this test strongly rules out that dark matter halos exist. In order to explain the observed rotation curves of galaxies, effective gravitation needs to become non-Newtonian below an acceleration threshold which is Milgrom’s constant. This concept is applied for the first time to simulate galaxy formation and evolution without dark matter particles, leading to remarkably simple and straightforward understanding of galaxies and their observed dynamics. The first steps are beginning to uncover a new cosmological model which may differ significantly from the LCDM one. Milgromian dynamics predicts a new physical phenomenon, the external field effect, and it is shown that astronomical data indeed bear evidence for this phenomenon, which is strictly non-Newtonian.