Using gravitational lens geometry to measure cosmological parameters

Abstract

We develop a technique for measuring cosmological parameters ([omega]M and w) using gravitational lens geometry, source and lens redshifts, and the velocity dispersion of the lensing galaxy. This technique makes use of the relation [theta][sub]E = 4[pi]... where the critical radius [theta][sub]E and the one-dimensional velocity dispersion of the lensing galaxy [sigma]v are observable and the angular diameter distance ratio D[sub]LS/D[sub]S is related to the source and lens redshifts Z[source] and Z[lens] through the cosmological model. We assess the feasibility of this technique by examining the dependence of that ratio on cosmological parameters, doing a Monte Carlo simulation with a singular isothermal sphere lens galaxy, and estimating the error due to the asymmetry of real lenses. We conclude that the method is feasible with a large lens sample and a nearly circular projected mass distribution. We expect errors of less than 0.1 in [omega]M for a flat universe with a cosmological constant and a lens sample selected so that the axial ratio f > 0.8 for each lens.