The hypothesis of the scale invariance of the macroscopic empty space, which intervenes through the cosmological constant, has led to new cosmological models. They show an accelerated cosmic expansion after the initial stages and satisfy several major cosmological tests. No unknown particles are needed.
Developing the weak-field approximation, we find that the here-derived equation of motion corresponding to Newton's equation also contains a small outward acceleration term. Its order of magnitude is about Newton's gravity ( being the mean density of the system and the usual critical density).
The new term is thus particularly significant for very low density systems. A modified virial theorem is derived and applied to clusters of galaxies. For the Coma Cluster and Abell 2029, the dynamical masses are about a factor of 5–10 smaller than in the standard case. This tends to leave no room for dark matter in these clusters.
Then, the two-body problem is studied and an equation corresponding to the Binet equation is obtained. It implies some secular variations of the orbital parameters. The results are applied to the rotation curve of the outer layers of the Milky Way. Starting backward from the present rotation curve, we calculate the past evolution of the Galactic rotation and find that, in the early stages, it was steep and Keplerian. Thus, the flat rotation curves of galaxies appear as an age effect, a result consistent with recent observations of distant galaxies by Genzel et al. and Lang et al.
Finally, in an appendix we also study the long-standing problem of the increase with age of the vertical velocity dispersion in the Galaxy. The observed increase appears to result from the new small acceleration term in the equation of the harmonic oscillator describing stellar motions around the Galactic plane.
Thus, we tend to conclude that neither dark energy nor dark matter seems to be needed in the proposed theoretical context.
Andrew Maeder "Dynamical Effects of the Scale Invariance of the Empty Space: The Fall of Dark Matter?" 849(2) The Astrophysical Journal 158 (November 10, 2017).