If it is hypothesized 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 lens 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 a 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
AðRÞ/R0:1^0:1 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 to 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.