Testing Bekenstein’s Relativistic MOND with Gravitational Lensing

With the recent elevation of Milgrom’s MOdified Newtonian Dynamics (MOND) to a relativistic theory, the Tensor-Vector-Scalar (TeVeS) theory of Bekenstein, a theory of gravity now exists which does not require dark matter and is consistent with fundamental relativistic principles. However, it remains challenging numerically and analytically to tackle the non-linear equations of TeVeS, which makes many of its properties obscure. Here we make detailed predictions for gravitational lensing in relativistic MOND for spherically symmetric lenses. We first show that a reasonable TeVeS model with a cosmological constant can fit the distance-redshift relation from supernova data, and so describe the background cosmology. We then derive the deflection angle, convergence and shear for the point lens and the Hernquist galaxy profile, and study their amplification patterns. Applying our analytical models we fit galaxyquasar lenses in the CASTLES sample. We do this by fitting the observed Einstein ring sizes, or the image positions, or the flux ratios. In all cases we consistently find that a good fit requires a large range of values of the acceleration scale a0, which should be a universal constant in MOND/TeVeS. This problem is not limitted to a specific choice of the force law, or the μ-function.