Can the relativistic field theory version of modified Newtonian dynamics avoid dark matter on galactic scales?

A fully relativistic analysis of gravitational lensing in tensor-vector-scalar (TeVeS) theory is presented. By estimating the lensing masses for a set of six lenses from the CASTLES database, and then comparing them to the stellar mass, the deficit between the two is obtained and analyzed. Considering a parametrized range for the TeVeS function mu(y), which controls the strength of the modification to gravity, it is found that on galactic scales TeVeS requires additional dark matter with the commonly used mu(y). A soft dependence of the results on the cosmological framework and the TeVeS free parameters is discussed. For one particular form of mu(y), TeVeS is found to require very little dark matter. This choice is however ruled out by rotation curve data. The inability to simultaneously fit lensing and rotation curves for a single form of mu(y) is a challenge to a no dark matter TeVeS proposal.