Abstract: The basis of the scale invariant theory is presented. While scale invariance is absent in Universe models with mean density ρ ≥ ρc, models of lower densities do experience some effects. The resulting cosmological models show an accelerated expansion not far from that of the LCDM models. A new equation of motion was also derived in this context. It contains an additional minor acceleration term which favors collapse during a contraction, and outwards acceleration during an expansion. This equation predicted, back in 2019, that the growth of initial density fluctuations is boosted, as seen with JWST observations of massive high-redshift galaxies. Dark matter (DM) is not needed. I will then review a series of positive observational tests about the dynamics of clusters of galaxies, galaxy rotation and wide binaries stars, without any fitting parameter. Last but not least, scale invariance also naturally reconciles the total mass and the stellar mass of galaxies acting as strong lenses, both at high redshift (JWST-ER1) and low redshift (SLACS). Thus, gravitation endowed with an additional symmetry, scale invariance, appears as a possibility to be further investigated.