Empirical constraints on alternative gravity theories from gravitational lensing

If it is hypothesized that there is no dark matter, then some alternative g ravitational theory must take the place of general relativity (GR) on the l argest scales. Dynamical measurements can be used to investigate the nature of such a theory, but only where there is visible matter. Gravitational le nsing is potentially a more powerful probe as it can be used to measure def lections far from the lens and for sufficiently large separations, allow it to be treated as a point-mass. Microlensing within the local group does no t yet provide any interesting constraints. as only images formed close to t he deflectors are appreciably magnified, but stacking of multiple light-cur ves 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 S ky Survey (SDSS) commissioning data used here to constrain the deflection l aw of galaxies to be A(R)proportional toR(0.1+/-0-1) for impact parameters in the range 50kpc less than or similar to R less than or similar to 1 Mpc. Together with observations of flat rotation curves. these results imply th at. in any gravitational theory, photons must experience (close to) twice t he deflection of massive particles moving at the speed of light (at least o n 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 ind ependent confirmation that galaxies are dark matter-dominated; conversely, azimuthal symmetry of the shear signal would rule out the typically ellipso idal haloes predicted by most simulations of structure formation.