Probing the dark energy with strong lensing by clusters of galaxies

Observations of clusters of galaxies that gravitationally lens faint background galaxies can probe the amount and the equation of state, w(X), of the dark energy (quintessence) in the universe. Provided that the mass profile and the mass normalization of the cluster are determined, it is possible to constrain the cosmological parameters that enter the lensing equations by means of the angular diameter distances, by locating (either by observations of giant arcs and magnification bias effect) the critical lines corresponding to known redshift source populations of galaxies. This method can help to distinguish between accelerating and decelerating models of the universe. Furthermore, since the position of critical lines is affected, especially in low-matter density universes, by the properties of quintessence, the observations of a suitable number of lensing clusters at intermediate redshifts can determine the equation of state. A very preliminary application of the method to the cluster CL 0024 + 1654 seems to support a flat accelerating universe dominated by dark energy.