Particles of the cosmic radiation, electrons and nuclei,
transport a dominant positive electric charge. A tiny fraction of these particles of extremely high energies in favorable conditions overflow from galaxies. The overflowing of positively charged cosmic nuclei into the intergalactic space uncovers an equal amount of negative charge in the parent galaxy. Negative charge is mainly stored by quiescent electrons. After adequate particle propagation neither the negative electric charge located in the galaxies nor the
positive electric charge of the overflowed cosmic nuclei can be neutralized due to the enormous distances.
In several ways it is proved that the total electric charge retained by clusters of galaxies after an appropriate time interval generate a repulsive force between clusters which overwhelms gravity. After a few billions years of electrostatic repulsion, peripheral clusters attain relativistic velocities and their mutual distances increase accordingly. Several facts suggest that the expansion of the universe, as determined by optical observations since a century, has been caused by the electrostatic repulsion of the positively charged cosmic nuclei overflowed from galaxy clusters.