Constraining the Cosmological Parameters using Strong Lensing

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  • 29 March 2001
Abstract
We investigate the potentiality of using strong lensing clusters to constrain the cosmological parameters \Omega_m and \Omega_\lambda. The existence of a multiple image system with known redshift allows, for a given (\Omega_m,\Omega_\lambda) cosmology, absolute calibration of the total mass deduced from lens modelling. Recent Hubble Space Telescope (HST) observations of galaxy clusters reveal a large number of multiple images, which are predicted to be at different redshifts. If it is possible to measure spectroscopically the redshift of many multiple images then one can in principle constrain (\Omega_m, \Omega_\lambda) through ratios of diameter angular distances, independently of any external assumptions. For a regular/relaxed cluster observed by HSTwith 3 multiple image systems, each with different spectroscopic redshifts, we show by analytic calculation that the following uncertainties can be expected: \Omega_m=0.3 +/- 0.25, \Omega_\lambda=0.7 +/- 0.5 or \Omega_m=1. +/- 0.4, \Omega_\lambda=0. +/-1.1 for the two most popular world models. Numerical tests on simulated data confirm the good constraints obtainable by this method, even in the case of more realistic cluster potentials, such as bimodal clusters, or when including galaxies perturbation. These constraints can be improved if more than 3 multiple images with spectroscopic redshifts are observed, or by combining the results from different clusters. Finally, combining such results with other cosmological tests should improve our knowledge on the cosmological world models.

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