Testing Bekenstein's Relativistic MOND gravity with Lensing Data

Abstract

We propose to use multiple-imaged gravitational lenses to set limits on gravity theories without dark matter, specificly TeVeS (Bekenstein 2004), a theory which is consistent with fundamental relativistic principles and the phenomenology of MOdified Newtonian Dynamics (MOND) theory. After setting the framework for lensing and cosmology, we derive analytically the deflection angle for the point lens and the Hernquist galaxy profile, and fit galaxy-quasar lenses in the CASTLES sample. We do this with three methods, fitting the observed Einstein ring sizes, the image positions, or the flux ratios. In all cases we consistently find that stars in galaxies in MOND/TeVeS provide adequate lensing. Bekenstein's toy $μ$ function provides more efficient lensing than the standard MOND $μ$ function. But for a handful of lenses [indicated in Table 2,3, fig 16] a good fit would require a lens mass orders of magnitude larger/smaller than the stellar mass derived from luminosity unless the modification function $μ$ and modification scale $a_0$ for the universal gravity were allowed to be very different from what spiral galaxy rotation curves normally imply. We discuss the limitation of present data and summarize constraints on the MOND $μ$ function. We also show that the simplest TeVeS "minimal-matter" cosmology, a baryonic universe with a cosmological constant, can fit the distance-redshift relation from the supernova data, but underpredicts the sound horizon size at the last scattering. We conclude that lensing is a promising approach to differentiate laws of gravity (see also astro-ph/0512425).