Gravitational Lensing Statistics as a Probe of Dark Energy

Abstract

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 $Ω_x$ and its equation of state $ω_x = p_x/ρ_x$. It is shown that, the larger the dark energy density is and the more negative its pressure is, the higher the gravitational lensing probability is. This fact can provide an independent constraint for dark energy.