  We model the nonlinear growth of cosmic structure in different dark energy
models, using large volume N-body simulations. We consider a range of
quintessence models which feature both rapidly and slowly varying dark energy
equations of state, and compare the growth of structure to that in a universe
with a cosmological constant. The adoption of a quintessence model changes the
expansion history of the universe, the form of the linear theory power spectrum
and can alter key observables, such as the horizon scale and the distance to
last scattering. The difference in structure formation can be explained to
first order by the difference in growth factor at a given epoch; this scaling
also accounts for the nonlinear growth at the 15% level. We find that
quintessence models which feature late $(z<2)$, rapid transitions towards
$w=-1$ in the equation of state, can have identical baryonic acoustic
oscillation (BAO) peak positions to those in $\Lambda$CDM, despite being very
different from $\Lambda$CDM both today and at high redshifts $(z \sim 1000)$.
We find that a second class of models which feature non-negligible amounts of
dark energy at early times cannot be distinguished from $\Lambda$CDM using
measurements of the mass function or the BAO. These results highlight the need
to accurately model quintessence dark energy in N-body simulations when testing
cosmological probes of dynamical dark energy.
