2014A&A...568L...2S

Strong gravitational lensing of sources with different redshifts has been used to determine cosmological distance ratios, which in turn depend on the expansion history. Hence, such systems are viewed as potential tools for constraining cosmological parameters. Here we show that in lens systems with two distinct source redshifts, of which the nearest one contributes to the light deflection toward the more distant one, there exists an invariance transformation that leaves all strong-lensing observables unchanged (except for the product of time delay and Hubble constant), generalizing the well-known mass-sheet transformation in single-plane lens systems. The transformation preserves the relative location of mass and light. All time delays (from sources on both planes) scale with the same factor - time-delay ratios are therefore invariant under the mass-sheet transformation. Changing cosmological parameters, and thus distance ratios, is essentially equivalent to such a mass-sheet transformation. As an example, we discuss the double-source plane system SDSSJ0946+1006, which has recently been studied by Collett and Auger, and show that variations of cosmological parameters within reasonable ranges lead to only a weak mass-sheet transformation in both lens planes. Hence, the ability to extract cosmological information from such systems depends heavily on the ability to break the mass-sheet degeneracy.