We present constraints on the equation of state of dark energy , w , and the total matter density , \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 \Omega _ { \mathrm { M } } = 0.33 _ { -0.26 } ^ { +0.33 } for a flat \Lambda CDM cosmology .
Combining with a CMB prior from Planck , we find w = -1.17 ^ { +0.20 } _ { -0.21 } 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 .