  If it is hypothesised that there is no dark matter then some alternative
gravitational theory must take the place of general relativity (GR) on the
largest scales. Dynamical measurements can be used to investigate the nature of
such a theory, but only where there is visible matter. Gravitational lensing is
potentially a more powerful probe as it can be used to measure deflections far
from the deflector, and, for sufficiently large separations, allow it to be
treated as a point-mass. Microlensing within the local group does not yet
provide any interesting constraints, as only images formed close to the
deflectors are appreciably magnified, but stacking of multiple light-curves and
observations of microlensing on cosmological scales may be able to discriminate
between GR and non-dark matter theories. Galaxy-galaxy lensing is likely to be
an even more powerful probe of gravity, with the Sloan Digital Sky Survey
(SDSS) commissioning data used here to constrain the deflection law of galaxies
to be A(R) propto R^(0.1 +/- 0.1) for impact parameters in the range 50 kpc < R
< 1 Mpc. Together with observations of flat rotation curves, these results
imply that, in any gravitational theory, photons must experience (close to)
twice the deflection of massive particles moving at the speed of light (at
least on these physical scales). The full SDSS data-set will also be sensitive
to asymmetry in the lensing signal and variation of the deflection law with
galaxy type. A detection of either of these effects would represent an
independent confirmation that galaxies are dark matter-dominated; conversely
azimuthal symmetry of the shear signal would rule out the typically ellipsoidal
haloes predicted by most simulations of structure formation.
