  We propose a relativistic model of dark matter reproducing at once the
concordance cosmological model $\Lambda$-Cold-Dark-Matter ($\Lambda$-CDM) at
cosmological scales, and the phenomenology of the modified Newtonian dynamics
(MOND) at galactic scales. To achieve this we postulate a non-standard 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 non-relativistic 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.
