Cosmological parameters from multiple-arc gravitational lensing systems. I. Smooth lensing potentials

We describe a new approach for the determination of cosmological parameters using gravitational lensing systems with multiple arcs. We exploit the fact that a given cluster can produce multiple arcs from sources over a broad range in redshift. The coupling between the critical radius of a single are and the projected mass density of the lensing cluster can be avoided by considering the relative positions of two or more arcs. Cosmological sensitivity appears through the angular size-redskift relation. We present a simple analytic argument for this approach using an axisymmetric, power-law cluster potential. In this case, the relative positions of the arcs can be shown to depend only on the ratios of the angular size distances of the source and the distances between the lens and source. Provided that the astrometric precision approaches similar to 0." 01 (e.g., via the Hubble Space Telescope) and the redshifts of the arcs are known, we show that the system can, in principle, provide cosmological information through the angular size-redshift relation. Next we consider simulated data constructed using a more general form for the potential, realistic sources and an assumed cosmology. We present a method for simultaneously inverting the lens and extracting the cosmological parameters. The input data required are the image and measured redshifts for the arcs. The technique relies on the conservation of surface brightness in gravitationally lensed systems. We find that for a simple lens model, our approach can recover the cosmological parameters assumed in the construction of the simulated images.