Like in the static case, weak gravitational lensing from large-scale structure will actually depend on , whereas galaxy clustering will arise only from the non-relativistic potential . By combining information on the matter overdensity at a given redshift (obtained by measuring the peculiar velocity field) and on the weak lensing maps, Zhang et al.  proposed a clever method to observationally estimate . This allowed Reyes et al.  to use luminous red galaxies in the SDSS survey in to exclude one model from the original TeVeS theory (Section 7.3) with the original function of , thus explicitly showing how such measurements could be a possible future smoking-gun for all theories based on dynamical vector fields. But note that other MOND theories such as BIMOND would not be affected by such measurements.
However, let us finally note a caveat in the interpretation of the weak lensing shear map in the context of relativistic MOND. While intercluster filaments negligibly contribute to the weak lensing signal in GR, a single filament inclined by from the line of sight can cause substantial distortion of background sources pointing toward the filament’s axis in relativistic MOND theories . Since galaxies are generally embedded in filaments or are projected on such structures, this contribution should be taken into account when interpreting weak lensing data. This additional difficulty for interpreting weak-lensing data in MOND is not only true for filaments, but more generally for all low-density structure such as sheets and voids.
Living Rev. Relativity 15, (2012), 10
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