Doubling Strong Lensing as a Cosmological Probe
  Strong gravitational lensing provides a geometric probe of cosmology in a
unique manner through distance ratios involving the source and lens. This is
well known for the time delay distance derived from measured delays between
lightcurves of the images of variable sources such as quasars. Recently, double
source plane lens systems involving two constant sources lensed by the same
foreground lens have been proposed as another probe, involving a different
ratio of distances measured from the image positions and fairly insensitive to
the lens modeling. Here we demonstrate that these two different sets of strong
lensing distance ratios have strong complementarity in cosmological leverage.
Unlike other probes, the double source distance ratio is actually more
sensitive to the dark energy equation of state parameters $w_0$ and $w_a$ than
to the matter density $\Omega_m$, for low redshift lenses. Adding double source
distance ratio measurements can improve the dark energy figure of merit by 40%
for a sample of fewer than 100 low redshift systems, or even better for the
optimal redshift distribution we derive.
