  We explore the use of strong lensing by galaxy clusters to constrain the dark
energy equation of state and its possible time variation. The cores of massive
clusters often contain several multiply imaged systems of background galaxies
at different redshifts. The locations of lensed images can be used to constrain
cosmological parameters due to their dependence on the ratio of angular
diameter distances. We employ Monte-Carlo simulations of cluster lenses,
including the contribution from substructures, to assess the feasibility of
this potentially powerful technique. At the present, parametric lens models use
well motivated scaling relations between mass and light to incorporate cluster
member galaxies, and do not explicitly model line-of-sight structure. Here, we
quantify modeling errors due to scatter in the cluster galaxy scaling relations
and un-modeled line-of-sight halos. These errors are of the order of a few
arcseconds on average for clusters located at typical redshifts (z ~ 0.2 -
0.3). Using Bayesian Markov Chain Monte-Carlo techniques, we show that the
inclusion of these modeling errors is critical to deriving unbiased constraints
on dark energy. However, when the uncertainties are properly quantified, we
show that constraints competitive with other methods may be obtained by
combining results from a sample of just 10 simulated clusters with 20 families
each. Cosmography with a set of well studied cluster lenses may provide a
powerful complementary probe of the dark energy equation of state. Our
simulations provide a convenient method of quantifying modeling errors and
assessing future strong lensing survey strategies.
