Strong gravitational lensing and dark energy

We investigate the statistics of gravitational lenses in flat, low-density cosmological models with different cosmic equations of state omega. We comp ute the lensing probabilities as a function of image separation theta using a lens population described by the mass function of Jenkins et al. and mod eled as singular isothermal spheres on galactic scales and as Navarro, Fren k, and White halos on cluster scales. It is found that COBE-normalized mode ls with omega > -0.4 produce too few arcsecond-scale lenses in comparison w ith the Jodrell-VLA Astrometric Survey (JVAS) and the Cosmic Lens All-Sky S urvey (CLASS), a result that is consistent with other observational constra ints on omega. The wide-separation (theta greater than or similar to 4 ") l ensing rate is a particularly sensitive probe of both omega and the halo ma ss concentration. The absence of these systems in the current JVAS/ CLASS d ata excludes highly concentrated halos in omega less than or similar to -0. 7 models. The constraints can be improved by ongoing and future lensing sur veys of greater than 10(5) sources.