  The Scale Invariant Vacuum (SIV) theory rests on the basic hypothesis that
the macroscopic empty space is scale invariant. This hypothesis is applied in
the context of the Integrable Weyl Geometry, where it leads to considerable
simplifications in the scale covariant cosmological equations. After an initial
explosion and a phase of braking, the cosmological models show a continuous
acceleration of the expansion. Several observational tests of the SIV cosmology
are performed: on the relation between $H_0$ and the age of the Universe, on
the $m-z$ diagram for SNIa data and its extension to $z=7$ with quasars and
GRBs, and on the $H(z)$ vs. $z$ relation. All comparisons show a very good
agreement between SIV predictions and observations. Predictions for the future
observations of the redshift drifts are also given. In the weak field
approximation, the equation of motion contains, in addition to the classical
Newtonian term, an acceleration term (usually very small) depending on the
velocity. The two-body problem is studied, showing a slow expansion of the
classical conics. The new equation has been applied to clusters of galaxies, to
rotating galaxies (some proximities with Modifies Newtonian Dynamics, MOND, are
noticed), to the velocity dispersion vs. the age of the stars in the Milky Way,
and to the growth of the density fluctuations in the Universe. We point out the
similarity of the mechanical effects of the SIV hypothesis in cosmology and in
the Newtonian approximation. In both cases, it results in an additional
acceleration in the direction of motions. In cosmology, these effects are
currently interpreted in terms of the dark energy hypothesis, while in the
Newtonian approximation they are accounted for in terms of the dark matter (DM)
hypothesis. These hypotheses appear no longer necessary in the SIV context.
