Gravitational Lenses and Unconventional Gravity Theories

We study gravitational lensing by clusters of galaxies in the context of the generic class of unconventional gravity theories of the scalar--tensor type. For positive energy scalar fields with any dynamics, the bending of light by a weakly gravitating system (galaxy or cluster) is always smaller than the bending predicted by general relativity for the mass of visible and hitherto undetected matter (but excluding the scalar field energy). The same conclusion obtains within general relativity if a nonnegligible part of the mass in clusters is in coherent scalar fields, {\it i.e.\/} Higgs fields. Thus the observational claim that clusters of galaxies deflect light much more strongly than would be expected from the observable matter contained by them, cannot be interpreted in terms of some scalar-tensor unconventional gravity theory with no dark matter. 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 dynamically determined mass significantly exceeds the lensing mass suggested by general relativity, would be very problematic for the dark matter picture, but would be entirely consistent with unconventional scalar--tensor gravity.