  The next generation mass probes will obtain information on non--linear power
spectra P(k,z) and their evolution, allowing us to investigate the nature of
Dark Energy. To exploit such data we need high precision simulations, extending
at least up to scales of k 10 h/Mpc, where the effects of baryons can no longer
be neglected.
  In this paper, we present a series of large scale hydrodynamical simulations
for LCDM and dynamical Dark Energy (dDE) models, in which the equation of state
parameter is z-dependent. The simulations include gas cooling, star formation
and Supernovae feedback. They closely approximate the observed star formation
rate and the observationally derived star/Dark Matter mass ratio in collapsed
systems. Baryon dynamics cause spectral shifts exceeding 1% at k > 2-3 h/Mpc
compared to pure n-body simulations in the LCDM simulations. This agrees with
previous studies, although we find a smaller effect (~50%) on the power
spectrum amplitude at higher k's. dDE exhibits similar behavior, even though
the dDE simulations produce ~20% less stars than the analogous LCDM
cosmologies. Finally, we show that the technique introduced in Casarini et al.
to obtain spectra for any $w(z)$ cosmology from constant-w models at any
redshift still holds when gas physics is taken into account. While this
relieves the need to explore the entire functional space of dark energy state
equations, we illustrate a severe risk that future data analysis could lead to
misinterpretation of the DE state equation.
