Abstract.A simple model for interaction of dark particles with matter based on resonance behavior in a three-body system is proposed. The model describes resonant amplification of effective interaction between two massive bodies at large distances between them. The phenomenon is explained by catalytic action of dark particles rescattering at a system of two heavy bodies which are understood here as the big stellar objects. Resonant amplification of the effective interaction between the two heavy bodies imitates the increase in their mass while their true gravitational mass remains unchanged. Such increased interaction leads to more pronounced gravitational lensing of bypassing light. It is shown that effective interaction between the heavy bodies is changed at larger distances and can transform into repulsive action.
IntroductionIt is well known, that the dark matter mystery emerged at the analysis of astronomical data when considerable discrepancy between orbital velocities of stellar objects at periphery of large galaxies compared to velocities calculated for usual gravitational fields has been found. This phenomenon was explained by the dark matter action that resulted in increased mass of such stellar objects. Discovered effect of gravitational lensing supported such assumption [1,2].In this presentation a model for resonance amplification of interaction between two stellar objects is proposed. The amplification is stimulated by additional interaction of the massive objects with dark matter particles (hereinafter dark particles). Our consideration is conducted in the framework of non-relativistic quantum theory of scattering in the three-body system, more exactly, for describing the interactions of two heavy bodies in presence of a dark particle of a very small mass. The solutions distinctly demonstrate that the effective interaction of these massive objects has the resonance behavior with the changing of distance between them.So, at relatively small distances the catalytic amplification is negligibly small and the effective interaction here coincides with the direct (gravitational) interaction between the heavy bodies. At larger distances, the catalytic action of the dark particles increases and the effective interaction between the heavy bodies also increases. At even larger distances, the catalytic action becomes smaller and then negative; so instead of attraction between the heavy bodies, it may cause their repulsion. The last to a certain extent would imitate the effects of dark energy.We assume that the dark particles do not interact with each other; the massive bodies interact not only via gravity, but also through exchange of dark particles. For simplicity, we would not consider the three-body type forces.