In the search for the nature of dark energy most cosmological probes measure
simple functions of the expansion rate. While powerful, these all involve
roughly the same dependence on the dark energy equation of state parameters,
with anticorrelation between its present value w_0 and time variation w_a.
Quantities that have instead positive correlation and so a sensitivity
direction largely orthogonal to, e.g., distance probes offer the hope of
achieving tight constraints through complementarity. Such quantities are found
in strong gravitational lensing observations of image separations and time
delays. While degeneracy between cosmological parameters prevents full
complementarity, strong lensing measurements to 1% accuracy can improve
equation of state characterization by 15-50%. Next generation surveys should
provide data on roughly 10^5 lens systems, though systematic errors will remain
challenging.Comment: 7 pages, 5 figure