The positive electric charge transported by the cosmic radiation while migrating from the interiors of galaxy clusters toward the outer intergalactic space, slowly but inevitably, uncovers a negative electric charge of the same amount inside galaxy clusters, where it is mostly retained. Electrons constitute the negative electric charge inside galaxy clusters. The negative charge and the positive one of the overflowed cosmic nuclei in the intergalactic space cannot be neutralized due to the separating, huge distances. After time intervals of a few billion years, electrostatic repulsion among galaxy clusters initiates to contrast gravity and, at longer time spans, dominates.  The electrostatic repulsion among galaxy clusters, which always store negative electric charges, determines in a few billion years, a general receding motion of cosmic matter, including smaller celestial bodies dragged in by galaxy clusters. It will be proved that the general receding motion of cosmic matter occurs with increasing velocities of galaxy clusters as far as the corresponding distances from the Earth augment.