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We study gravitational lensing by clusters of galaxies in the context of the generic class of unconventional gravity theories which describe gravity in terms of a metric and one or more scalar fields (called here scalar-tensor theories). We conclude that, if the scalar fields have positive energy, then whatever their dynamics, the bending of light by a weakly gravitating system, like a galaxy or a cluster of galaxies, cannot exceed the bending predicted by general relativity for the mass of visible and hitherto undetected matter (but excluding the scalar field's energy). Thus using general relativity to interpret gravitational lensing observations can only underestimate the mass present in stars, gas, and dark matter. The same conclusion obtains within general relativity if a non-negligible part of the mass in clusters is in the form of coherent scalar fields, i.e., Higgs fields. The popular observational claim that clusters of galaxies deflect light much more strongly than would be expected from the observable matter contained by them, if it survives, cannot be interpreted in terms of some scalar-tensor unconventional gravity theory with no dark matter. And if the observations eventually show that the matter distribution inferred via general relativity from the lensing is very much like that determined from the dynamics of test objects, then scalar-tensor unconventional gravity will be irrelevant for understanding the mass discrepancy in clusters. However, even a single system in which the dynamical mass determined from virial methods significantly exceeds the lensing mass as determined by general relativity would be very problematic for the dark matter picture but would be entirely consistent with unconventional scalar-tensor gravity theory.
Bekenstein et al. (Fri,) studied this question.