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-like53
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
fluid54.)
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:
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).
http://www.livingreviews.org/lrr-2012-10 |
Living Rev. Relativity 15, (2012), 10
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