An empty Universe would be scale invariant, as shown by both Maxwell equations and General Relativity.
The question arises on how much matter is necessary to break scale invariance in the Universe.
On the basis of scale invariant models based on expressions derived by Dirac (1973), we show that scale invariant effects rapidly decline to zero for cosmological models with a density between zero and the critical one. For a density parameter Omega_m=0.3, some limited effects are remaining, which correspond to the observed accelerated expansion. Several cosmological tests are consistent, e.g. the growth of density fluctuations is boosted in the scale invariant context, a large M/L ratio is derived for clusters of galaxies, flat rotation curves are predicted in galaxies with a proper account of the radial acceleration relation (RAR).
André Maeder (Geneva): Possible scale invariant effects in our low density Universe
