We perform a set of ray-tracing simulations, using numerical cluster models, aiming at evaluating how the galaxy cluster efficiency for producing strong lensing events changes in different cosmological models with dark energy. The sample of investigated clusters for which we present our results here is composed by 7 dark matter halos. Each of them was simulated in 8 different cosmological models with constant and time-variable equation of state of dark energy. For all the clusters in the sample, we have measured the lensing cross sections for producing giant arcs, i.e. arcs having a minimum length-to-width ratio. We find that the lensing cross section for giant arcs is sensitive to the equation of state of quintessence. Indeed, the optical depth, which can be translated into a number of arcs by multiplying by the correct density of source galaxy on the sky, spans more than one order of magnitude among different cosmological models.
