Abstract. We introduce analytical expressions for a pseudo fully analytical elliptical projected Navarro, Frenk & White (NFW) mass profile to be used in lensing equations. We propose a formalism that incorporates the ellipticity into the expression for the lens potential, producing a pseudo-elliptical mass distribution. This approach can be implemented to any circular mass profile for which the projected mass profile Σ(r) and the deflection angle profile α(r) both have analytical expressions; however the potential does not necessarily need to take an analytical form. We apply this new formalism to the NFW mass distribution and study how well this pseudo-elliptical NFW model describes an elliptical mass distribution. We conclude that the pseudoelliptical NFW model is a good description of elliptical mass distributions provided that the ellipticity of the projected mass distribution is < ∼ 0.4, although with a slightly boxy distribution.

Abstract. We investigate the potential of using strong lensing clusters to constrain the cosmological parameters Ωm and Ω λ . The existence of a multiple image system with known redshift allows, for a given (Ωm, Ω λ ) 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 redshifts of many multiple images then one can in principle constrain (Ωm, Ω λ ) through ratios of angular diameter distances, independently of any external assumptions. For a regular/relaxed cluster observed by HST with 3 multiple image systems, each with different spectroscopic redshifts, we show by analytic calculation that the following uncertainties can be expected: Ωm = 0.30 ± 0.11, Ω λ = 0.70 ± 0.23 or Ωm = 1.00 ± 0.17, Ω λ = 0.00 ± 0.48 for the two most popular world models. Numerical tests on simulated data confirm these good constraints, even in the case of more realistic cluster potentials, such as bimodal clusters, or when including perturbations by galaxies. To investigate the sensitivity of the method to different mass profiles, we also use an analytic "pseudo-elliptical" Navarro et al. profile in the simulations. These constraints can be improved if more than 3 multiple images with spectroscopic redshifts are observed, or by combining the results from different clusters. Some prospects on the determination of the cosmological parameters with gravitational lensing are given.

Abstract. In this Letter we present a detailed study of the lensing configuration in the cluster Abell 2218. Four multipleimages systems with measured spectroscopic redshifts have been identified in this cluster. These multiple images are very useful to constrain accurately the mass distribution in the cluster core, but they are also sensitive to the value of the geometrical cosmological parameters of the Universe. Using a simplified maximum likelihood analysis we find 0 < Ω M < 0.30 assuming a flat Universe, and 0 < Ω M < 0.33 and w < −0.85 for a flat Universe with dark energy. Interestingly, an Einstein-de Sitter model is excluded at more than 4σ. These constraints are consistent with the current constraints derived with CMB anisotropies or supernovae studies. The proposed method constitutes an independent test of the geometrical cosmological parameters of the Universe and we discuss the limits of this method and this particular application to Abell 2218. Application of this method with more sophisticated tools and to a larger number of clusters or with more multiple images constraints, will put stringent constraints on the geometrical cosmological parameters.