Gravitational lensing in modified Newtonian dynamics

Modified Newtonian dynamics (MOND) is an alternative theory of gravity that aims to explain large-scale dynamics without recourse to any form of dark matter. However the theory is incomplete, lacking a relativistic counterpart, and so makes no definite predictions about gravitational lensing. The most obvious form that MONDian lensing might take is that photons experience twice the deflection of massive particles moving at the speed of light, as in general relativity (GR). In such a theory there is no general thin-lens approximation (although one can be made for spherically-symmetric deflectors), but the three-dimensional acceleration of photons is in the same direction as the relativistic acceleration would be. In regimes where the deflector can reasonably be approximated as a single point-mass (specifically low-optical depth microlensing and weak galaxy-galaxy lensing), this naive formulation is consistent with observations. Forthcoming galaxy-galaxy lensing data and the possibility of cosmological microlensing have the potential to distinguish unambiguously between GR and MOND. Some tests can also be performed with extended deflectors, for example by using surface brightness measurements of lens galaxies to model quasar lenses, although the breakdown of the thin-lens approximation allows an extra degree of freedom. Nonetheless, it seems unlikely that simple ellipsoidal galaxies can explain both constraints. Further, the low-density universe implied by MOND must be completely dominated by the cosmological constant (to fit microwave background observations), and such models are at odds with the low frequency of quasar lenses. These conflicts might be resolved by a fully consistent relativistic extension to MOND; the alternative is that MOND is not an accurate description of the universe.