Origin of the logarithmic correction to the Newton's law in the presence of a homogeneous gas of wormholes

We suggest a new scenario in which the Universe starts its evolution with a fractal topological structure. This structure is described by a gas of wormholes. It is shown that the polarization of such a gas in external fields possesses a spatial dispersion, which results in a modification of the Newton's law. The dependence on scales is determined by the distribution of distances between throat ends. The observed in galaxies logarithmic correction confirms that the distribution has fractal properties. We also discus the possibility of restoring such a distribution from observations.