8 Gravitational Lensing in Relativistic MOND

The viable MOND theories from Section 7, although still mostly effective, have the great advantage of proving that constructing relativistic MOND theories is possible, and that it is thus possible to calculate from them the effects of gravitational lensing. But the non-uniqueness of the theories means that there is not really a unique prediction for gravitational lensing, especially in heavily–time-dependent configurations, or when the predictions of the theories for the expansion history of the universe deviate from the concordance model. As we have seen, some theories also deviate slightly from classical MOND predictions for dynamics of quasi-static systems, due to the presence of massive dark fields, and the same would of course happen for gravitational lensing. However, at the zeroth order, and in static weak-field configurations, we can make predictions for all theories whose expansion history would be similar to that of ΛCDM (see Section 9.1) and whose static weak-field limit is represented by a physical metric56 with Ψ = − Φ in Eq. 73View Equation (Φ obeying Eq. 17View Equation). In this case, the way the light propagates on the null geodesics of this metric is exactly the same in all these theories once Φ is known. What differs from GR is only the relation between Φ and the underlying mass distribution of the lens.

 8.1 Strong lensing by galaxies
 8.2 Weak lensing by galaxies
 8.3 Strong and weak lensing by galaxy clusters
 8.4 Weak lensing by large-scale structure

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