Model of dark matter and dark energy based on gravitational polarization

A model of dark matter and dark energy based on the concept of gravitational polarization is investigated. We propose an action in standard general relativity for describing, at some effective or phenomenological level, the dynamics of a dipolar medium, i.e. one endowed with a dipole moment vector, and polarizable in a gravitational field. Using first-order cosmological perturbations, we show that the dipolar fluid is undistinguishable from standard dark energy (a cosmological constant Λ) plus standard dark matter (a pressureless perfect fluid), and therefore benefits from the successes of the Λ cold-dark-matter scenario at cosmological scales. Invoking an argument of “weak clusterization” of the mass distribution of dipole moments, we find that the dipolar dark matter reproduces the phenomenology of the modified Newtonian dynamics at galactic scales. The dipolar medium action naturally contains a cosmological constant, and we show that if the model is to come from some fundamental underlying physics, the cosmological constant Λ should be of the order of a₀²/c⁴, where a₀ denotes the modified Newtonian dynamics constant acceleration scale, in good agreement with observations.