Observational tests in scale invariance I: galaxy clusters and rotation of galaxies

Galaxy velocities in clusters, rotation curves of galaxies, and "vertical" oscillations in the Milky Way currently show too high velocities with respect to the masses thought to be involved. While these velocity excesses are currently interpreted as the consequence of dark matter, it can also be naturally explained as a consequence of scale invariant theory, which rests on a very simple first principle: the addition of a new fundamental symmetry. In the present work, the case of scale invariance, present in General Relativity and Maxwell equations for the empty space without charge and current, is considered. Cosmological models predict a rapid decrease of these effects with increasing mean density up to the critical density, where they totally disappear. Starting from the scale invariant geodesic equation by Dirac (1973), for which a demonstration by an action principle is presented, a modified Newton equation is derived. The solutions of this equation are applied to clusters of galaxies, galactic rotation at different redshifts and "vertical" motions in the Milky Way. In this new framework, the convergence of theoretical predictions and observations, in different gravitational systems, epochs, mass range and spatial scales, opens interesting perspectives that deserve to be explored further.