Cosmological parameters from lenses distance ratio

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Strong lensing provides popular techniques to investigate the mass distribution of intermediate redshift galaxies, testing galaxy evolution and formation scenarios. It especially probes the background cosmic expansion, hence constraining cosmological parameters. The measurement of Einstein radii and central velocity dispersions indeed allows to trace the ratio Dₛ/Dₗs between the distance Dₛ from the observer to the source and the distance Dₗs from the lens to the source. We present an improved method to explicitly include the two - component structure in the galaxy lens modeling, in order to analyze the role played by the redshift and the model dependence on a nuisance parameter, Fₑ, which is usually marginalized in the cosmological applications. We show how to deal with these problems and carry on a Fisher matrix analysis to infer the accuracy on cosmological parameters achieved by this method.