Absence of the Fifth Force Problem in a Model with Spontaneously Broken Dilatation Symmetry

A scale invariant model containing dilaton $\phi$ and dust (as a model of matter) is studied where the shift symmetry $\phi\to\phi +const.$ is spontaneously broken at the classical level due to intrinsic features of the model. The dilaton to matter coupling "constant" $f$ appears to be dependent of the matter density. In normal conditions, i.e. when the matter energy density is many orders of magnitude larger than the dilaton contribution to the dark energy density, $f$ becomes less than the ratio of the "mass of the vacuum" in the volume occupied by the matter to the Planck mass. The model yields this kind of "Archimedes law" without any especial (intended for this) choice of the underlying action and without fine tuning of the parameters. The model not only explains why all attempts to discover a scalar force correction to Newtonian gravity were unsuccessful so far but also predicts that in the near future there is no chance to detect such corrections in the astronomical measurements as well as in the specially designed fifth force experiments on intermediate, short (like millimeter) and even ultrashort (a few nanometer) ranges. This prediction is alternative to predictions of other known models.