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

TL;DR

This paper proposes a new method to measure dark matter and dark energy densities using gravitational lens time delays and galaxy velocity dispersions, offering a potential cosmic standard ruler.

Contribution

It introduces a novel approach combining time delay and velocity dispersion measurements to constrain cosmological parameters.

Findings

Angular diameter distance is proportional to dt/sigma^2 for isothermal sphere lenses.

Simulations show promising constraints on dark matter and dark energy densities.

Future observations can significantly improve cosmological parameter estimates.

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.