Gravitational Lensing Statistics as a Probe of Dark Energy

By using the comoving distance, we derive an analytic expression for the optical depth of gravitational lensing, which depends on the redshift to the source and the cosmological model characterized by the cosmic mass density parameter Ω m , the dark energy density parameter Ω m and its equation of state ω x = p x /ρ x . It is shown that, the larger the dark energy density and the more negative its pressure, the higher is the gravitational lensing probability. This fact can provide an independent constraint for dark energy.