In a series of papers, Blanchet & Le Tiec [55, 56, 57, 58, 59, 60] have pushed
further the idea that the MOND phenomenology could arise from the fundamental
properties of a form of dark matter itself, by suggesting that dark matter could carry a
space-like^{53}
four-vector gravitational dipole moment , following the analogy between Milgrom’s law
and Coulomb’s law in a dieletric medium proposed by [56] (see Eq. 9) or between the
Bekenstein–Milgrom modified Poisson equation and Gauss’ law in terms of free charge density
(see Eq. 17). The dark matter medium is described as a fluid with mass current
(where is the equivalent of the mass density of the atoms in a dielectric medium, i.e., it is
the ordinary mass density of a pressureless perfect fluid, and is the four-velocity of the
fluid^{54}.)
endowed with the dipole moment vector (which will affect the total density in addition to the above
mass density ), with the following action [60]:

The equations of motion of the dark matter fluid are then gotten by varying the action w.r.t. the dipole moment variable and w.r.t. to the current , boiling down in the non-relativistic limit to:

where is the ordinary velocity of the fluid, is the gravitational field, and is the internal non-gravitational force field making the dark particles motion non-geodesic. What is more, the Poisson equation in the weak-field limit is recovered as: In order to then reproduce the MOND phenomenology in galaxies, the next step is the “weak-clustering hypothesis”, namely the fact that, in galaxies, the dark matter fluid does not cluster much () and is essentially at rest () because the internal force of the fluid precisely balances the gravitational force in such a way that the polarization field is precisely aligned with the gravitational one , and . The potential thus plays the role of the “MOND function”, and, e.g., choosing to determine it up to third order in expansion as then yields the desired MOND behavior in Eq. 103, with the “simple” -function (see Eqs. 42 and 49).This model has many advantages. The monopolar density of the dipolar atoms will play the role of CDM in the early universe, while the minimum of the potential naturally adds a cosmological constant term, thus making the theory precisely equivalent to the CDM model for expansion and large scale structure formation. The dark matter fluid behaves like a perfect fluid with zero pressure at first-order cosmological perturbation around a FLRW background and thus reproduces CMB anisotropies. Let us also note that, if the potential defining the internal force of the dipolar medium is to come from a fundamental theory at the microscopic level, one expects that the dimensionless coefficients in the expansion all be of order unity after rescaling by , thus naturally leading to the coincidence .

However, while the weak clustering hypothesis and stationarity of the dark matter fluid in galaxies are suppported by an exact and stable solution in spherical symmetry [58], it remains to be seen whether such a configuration would be a natural outcome of structure formation within this model. The presence of this stationary DM fluid being necessary to reproduce Milgrom’s law in stellar systems, this theory loses a bit of the initial predictability of MOND, and inherits a bit of the flexibility of CDM, inherent to invoking the presence of a DM fluid. This DM fluid could, e.g., be absent from some systems such as the globular clusters Pal 14 or NGC 2419 (see Section 6.6.3), thereby naturally explaining their apparent Newtonian behavior. However, the weak clustering hypothesis in itself might be problematic for explaining the missing mass in galaxy clusters, due to the fact that the MOND missing mass is essentially concentrated in the central parts of these objects (see Section 6.6.4).

Living Rev. Relativity 15, (2012), 10
http://www.livingreviews.org/lrr-2012-10 |
This work is licensed under a Creative Commons License. E-mail us: |