  In previous work [L. Blanchet and A. Le Tiec, Phys. Rev. D 78, 024031
(2008)], a model of dark matter and dark energy based on the concept of
gravitational polarization was investigated. This model was shown to recover
the concordance cosmological scenario (Lambda-CDM) at cosmological scales, and
the phenomenology of the modified Newtonian dynamics (MOND) at galactic scales.
In this article we prove that the model can be formulated with a simple and
physically meaningful matter action in general relativity. We also provide
alternative derivations of the main results of the model, and some details on
the variation of the action.
