Cosmological Constraints from the double source plane lens SDSSJ0946+1006

We present constraints on the equation of state of dark energy, $w$, and the total matter density, ${\mathrm{\Omega }}_{\mathrm{M}}$, derived from the double-source-plane strong lens SDSSJ0946+1006, the first cosmological measurement with a galaxy-scale double-source-plane lens. By modelling the primary lens with an elliptical power-law mass distribution, and including perturbative lensing by the first source, we are able to constrain the cosmological scaling factor in this system to be ${\beta }^{-1}=1.404\pm 0.016$, which implies ${\mathrm{\Omega }}_{\mathrm{M}}=0.33_{-0.26}^{+0.33}$ for a flat $\mathrm{\Lambda }$ cold dark matter ($\mathrm{\Lambda }$CDM) cosmology. Combining with a cosmic microwave background prior from Planck, we find $w$ = $-1.17_{-0.21}^{+0.20}$ assuming a flat $w$CDM cosmology. This inference shifts the posterior by 1$\sigma$ and improves the precision by 30 per cent with respect to Planck alone, and demonstrates the utility of combining simple, galaxy-scale multiple-source-plane lenses with other cosmological probes to improve precision and test for residual systematic biases.