  The phenomenology of the modified Newtonian dynamics (MOND) can be recovered
from a mechanism of "gravitational polarization" of some dipolar medium playing
the role of dark matter. We review a relativistic model of dipolar dark matter
(DDM) within standard general relativity to describe, at some effective level,
a fluid polarizable in a gravitational field. At first order in cosmological
perturbation theory, this model is equivalent to the concordance cosmological
scenario, or Lambda-cold dark matter (CDM) model. At second order, however, the
internal energy of DDM modifies the curvature perturbation generated by CDM.
This correction, which depends quadratically on the dipole, induces a new type
of non-Gaussianity in the bispectrum of the curvature perturbation with respect
to standard CDM. Recent observations by the Planck satellite impose stringent
constraints on the primordial value of the dipole field.
