Gravitational lenses in the dark Universe

Abstract

We discuss how different cosmological models of the Universe affect the probability that a background source has multiple images related by an angular distance $θ_E$ of the line of sight, \textit{i. e.}, the optical depth of gravitational lensing. We examine some cosmological models for different values of the density parameter $Ω_i$: i) the cold dark matter model, ii) the $Λ$CDM model, iii) the Bose-Einstein condensate dark matter model, iv) the Chaplygin gas model, v) the viscous fluid cosmological model and vi) the holographic dark energy model. We note that the dependence of the energy-matter content of the universe profoundly alters the frequency of multiple quasar image.