For TeVeS (Section 7.4) and GEA (Section 7.7), the growth of the spatial part of the vector perturbation in the course of cosmological evolution can successfully seed the growth of baryonic structures, just as dark matter does, and it is possible to reconstruct the gravitational field of the bullet cluster without any extra matter but with a substantial contribution from the vector field. However, why the dynamical evolution of the vector field perturbations would lead to precisely such a configuration remains unclear. Similarly, the massive scalar field of Section 7.6 or the monopolar part of the dipolar DM of Section 7.9 could, in principle, provide the off-centered missing mass too, but again, why they would appear distributed as they do remains unclear, especially in the case of dipolar DM, which is supposed to cluster only very weakly, and, in principle, not to appear as densely clustered. Whether the twin matter of BIMOND (Section 7.8) could help providing the right convergence map also remains to be seen, while for non-local models (Section 7.10), there is a strong dependence on the past light-cone, meaning that recently-disturbed systems, such as the Bullet, may be far from the static MOND limit (but in that case, it would not be clear why all the other clusters from Section 6.6.4 exhibit the same amount of residual missing mass). So, while the bullet cluster clearly does not represent the MOND-killer that it was supposed to be, explaining its convergence map remains an outstanding challenge for all MOND theories. However, the bullet cluster also represents an outstanding challenge to CDM (see Section 4.2), due to its high collision speed . In that respect, MOND is much more promising .
On the other hand, a comprehensive weak lensing mass reconstruction of the rich galaxy cluster Cl0024+17 at  has been argued to have revealed the first dark matter structure that is offset from both the gas and galaxies in a cluster. This structure is ringlike, located between and . It was, again, argued to be the result of a collision of two massive clusters 1 – 2 Gyr in the past, but this time along the line-of-sight. It has also been argued  that this offset was hard to explain in MOND. Assuming that this ringlike structure is real and not caused by instrumental bias or spurious effects in the weak lensing analysis (due, e.g., to the unification of strong and weak-lensing or to the use of spherical/circular priors), and that cluster stars and galaxies do not make up a high fraction of the mass in the ring (which would be too faint to observe anyway), it has been shown that, for certain interpolating functions with a sharp transition, this is actually natural in MOND . A peak in the phantom dark matter distribution generically appears close to the transition radius of MOND , especially when most of the mass of the system is well-contained inside this radius (which is the case for the cluster Cl0024+17). This means that the ring in Cl0024+17 could be the first manifestation of this pure MOND phenomenon, and thus be a resounding success for MOND in galaxy clusters. However, the sharpness of this phantom dark matter peak strongly depends on the choice of the -function, and for some popular ones (such as the “simple” -function) the ring cannot be adequately reproduced by this pure MOND phenomenon. In this case, a collisional scenario would be needed in MOND too, in order to explain the feature as a peak of cluster dark matter. Indeed, we already know that there is a mass discrepancy in MOND clusters, and we know that this dark matter must be in collisionless form (e.g., neutrinos or dense clumps of cold gas). So the results of the simulation with purely collisionless dark particles  would surely be very similar in MOND gravity. Again, it was shown that the density of missing mass was compatible with 2 eV ordinary neutrinos, like in most clusters with . Finally, let us note that strong lensing was also recently used as a robust probe of the matter distribution on scales of 100 kpc in galaxy clusters, especially in the cluster Abell 2390 . A residual missing mass was again found, compatible with the densities provided by fermionic hot dark matter candidates only for masses of 10 eV and heavier. All in all, the problem posed by gravitational lensing from galaxy clusters is thus very similar to the one posed by the temperature profiles of their X-ray emitting gas (Section 6.6.4), and remains one of the two main current problems of MOND, together with its problem at reproducing the CMB anisotropies (see Section 9.2).
Finally, let us note in passing that another (non-lensing) test of relativistic MOND theories in galaxy clusters has been performed by analysing the gravitational redshifts of galaxies in 7800 galaxy clusters , which were originally found to be difficult to reconcile with MOND: however, this original analysis assumed a distribution of residual missing mass in MOND by simply scaling down the Newtonian dynamical mass represented by a NFW halo by a factor 0.8, and the analysis confused the interpolating functions and (see Section 6.2). A subsequent analysis  showed that these gravitational redshifts were in accordance with relativistic MOND when the correct residual mass and acceptable -functions were used.
Living Rev. Relativity 15, (2012), 10
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