Gravity modification with Yukawa-type potential: dark matter and mirror gravity

The nature of the gravitational interaction between ordinary and dark matter is still open. Any deviation from universality or the Newtonian law also modifies the standard assumption of collisionless dark matter. On the other hand, obtaining a Yukawa-like large-distance modification of the gravitational potential is a nontrivial problem, that has so far eluded a consistent realization even at linearized level. We propose here a theory providing a Yukawa-like potential, by coupling non-derivatively the two metric fields related respectively to the visible and dark matter sectors, in the context of massive gravity theories where the local Lorentz invariance is broken by the different coexisting backgrounds. This gives rise to the appropriate mass pattern in the gravitational sector, producing a healthy theory with the Yukawa potential. Our results are of a special relevance in the scenario of dark matter originated from the mirror world, an exact duplicate of the ordinary particle sector.