  We make an exploratory study of how well dark energy models can be
constrained using lensed arcs at different redshifts behind cluster lenses.
Arcs trace the critical curves of clusters, and the growth of critical curves
with source redshift is sensitive to the dark-energy equation of state. Using
analytical models and numerically simulated clusters, we explore the key
factors involved in using cluster arcs as a probe of dark energy. We quantify
the sensitivity to lens mass, concentration and ellipticity with analytical
models that include the effects of dark energy on halo structure. We show with
simple examples how degeneracies between mass models and cosmography may be
broken using arcs at multiple redshifts or additional constraints on the lens
density profile. However we conclude that the requirements on the data are so
stringent that it is very unlikely that robust constraints can be obtained from
individual clusters. We argue that surveys of clusters, analyzed in conjunction
with numerical simulations, are a more promising prospect for arc-cosmography.
  We use such numerically simulated clusters to estimate how large a sample of
clusters/arcs could provide interesting constraints on dark energy models. We
focus on the scatter produced by differences in the mass distribution of
individual clusters. We find from our sample of simulated clusters that at
least 1000 pairs of arcs are needed to obtain constraints if the mass
distribution of individual clusters is taken to be undetermined. We discuss
several unsolved problems that need study to fully develop this method for
precision studies with future surveys.
