  Dark energy has a dramatic effect on the dynamics of the universe, causing
the recently discovered acceleration of the expansion. The dynamics are also
central to the behavior of the growth of large scale structure, offering the
possibility that observations of structure formation provide a sensitive probe
of the cosmology and dark energy characteristics. In particular, dark energy
with a time varying equation of state can have an influence on structure
formation stretching back well into the matter dominated epoch. We analyze this
impact, first calculating the linear perturbation results, including those for
weak gravitational lensing. These dynamical models possess definite observable
differences from constant equation of state models. Then we present a large
scale numerical simulation of structure formation, including the largest volume
to date involving a time varying equation of state. We find the halo mass
function is well described by the Jenkins et al. mass function formula. We also
show how to interpret modifications of the Friedmann equation in terms of a
time variable equation of state. The results presented here provide steps
toward realistic computation of the effect of dark energy in cosmological
probes involving large scale structure, such as cluster counts,
Sunyaev-Zel'dovich effect, or weak gravitational lensing.
