Gravitational lenses as cosmic rulers: density of dark matter and dark energy from time delays and velocity dispersions

Abstract

We show that a cosmic standard ruler can be constructed from the joint measurement of the time delay (dt) between gravitationally lensed quasar images and the velocity dispersion (sigma^2) of the lensing galaxy. This is specifically shown, for a singular isothermal sphere lens, where the angular diameter distance to the lens is proportional to dt/sigma^2. Using MCMC simulations we illustrate the constraints set in the density of dark matter and dark energy plane from future observations.