Phenomenology of dark matter via a bimetric extension of general relativity

We propose a relativistic model of dark matter reproducing at once the concordance cosmological model $\mathrm{\Lambda }$-cold-dark-matter ($\mathrm{\Lambda }\text{−}\mathrm{CDM}$) at cosmological scales and the phenomenology of the modified Newtonian dynamics (MOND) at galactic scales. To achieve this we postulate a nonstandard form of dark matter, consisting of two different species of particles coupled to gravity via a bimetric extension of general relativity and linked together through an internal vector field (a “graviphoton”) generated by the mass of these particles. We prove that this dark matter behaves like ordinary cold dark matter at the level of first-order cosmological perturbation, while a pure cosmological constant plays the role of dark energy. The MOND equation emerges in the nonrelativistic limit through a mechanism of gravitational polarization of the dark matter medium in the gravitational field of ordinary matter. Finally we show that the model is viable in the Solar System as it predicts the same parametrized post-Newtonian parameters as general relativity.