Résumé
Weak gravitational lensing perturbations have a non-negligible impact on strong lensing observables, and several degeneracies exist between the properties of the main lens, line of sight, and cosmology. In this work, we consider the impact of the line of sight on double-source-plane lenses (DSPLs), a rare class of lens systems in which two sources at different redshifts are lensed by the same foreground galaxy, and which enable competitive constraints on the dark energy equation of state. Generating and sampling statistically representative lines of sight from N-body simulations, we show that line-of-sight perturbations add a $\sim1\%$ uncertainty to measurements of the cosmological scaling factor $\eta$ (a ratio of angular diameter distance ratios), which is subdominant but non-negligible compared to the measurement error. We also show that the line-of-sight shear experienced by images of the two sources can differ significantly in both magnitude and direction. Including a line-of-sight error budget, we measure $w=-1.17^{+0.19}_{-0.21}$ from the Jackpot DSPL in combination with Planck. We show that the line of sight is expected to introduce an additional scatter in the constraints possible with a larger sample of DSPLs from Euclid, but that this scatter is subdominant compared to other sources of error.