Introduction

In the time since the discovery of the first multiply-imaged quasar (Walsh, Carswell & Weymann 1979), gravitational lensing has become one of the more powerful tools available to astronomers. The main advantage of lensing as an astronomical probe lies in its simplicity - the light deflection properties of a lens depend on just two things: its mass distribution and the nature of gravitational physics.

The success of general relativity (GR) - and, in the appropriate limits, Newtonian gravity - is such that lensing is almost always used to investigate the distribution of matter in the universe. The fact that, for example, cluster lensing cannot be explained by the visible galaxies and gas is then taken to be strong evidence for the preponderance of dark matter. There is, of course, a great deal of evidence that the universe is dark matter-dominated (e.g., Trimble 1987), but the lack of any non-gravitational detection of dark mass makes it an assumption that should continue to be tested by all available means.

The alternative possibility is that GR is only valid in the small-scale, large-acceleration regimes in which it has been experimentally (as opposed to observationally) tested. The majority of direct tests have been within the Solar system, but measurements of time delays in binary pulsar systems (Taylor et al. 1992) have also verified GR. The degeneracy between the form of the gravitational acceleration and the distribution of mass is such that GR remains an assumption on galactic (and greater) scales. If it is hypothesised that there is no dark matter, then it is possible to determine the nature of gravity on these large scales from lensing or dynamical observations. Aside from their tendency to rely on assumptions of equilibrium, dynamical measurements are subject to the more fundamental limitation that the gravitational field can only be probed in regions where there is visible matter. By contrast lensing can be used to measure gravitational effects well beyond the luminous extent of the deflector(s). Further, if such measurements can be made sufficiently far from the lens¹, its internal structure becomes unimportant, and the lensing data uniquely constrains the deflection law of a point-mass. This is a potentially powerful technique that only breaks down at angular scales so large that the effects of other deflectors along the line-of-sight become important.

These methods can be used to determine the deflection law of a point-mass empirically (Mortlock & Turner 2001a) or to test a particular theory. For example Mortlock & Turner (2001b) investigated gravitational lensing within the framework of modified Newtonian dynamics (MOND). A combined approach is taken here, using MOND as an illustrative example. After explaining the principles of the theory (Section 2), a robust deflection law is derived from galaxy-galaxy lensing data (Section 3). The future prospects for more rigorous tests are then discussed in Section 4.

© Copyright Astronomical Society of Australia 1997