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

Cosmological Constraints from the double source plane lens SDSSJ0946+1006