Imprints of Dark Energy on Cosmic Structure Formation I) Realistic
  Quintessence Models and the Non-Linear Matter Power Spectrum
  Dark energy as a quintessence component causes a typical modification of the
background cosmic expansion, which in addition to its clustering properties,
can leave a potentially distinctive signature on large scale structures. Many
previous studies have investigated this topic, particularly in relation to the
non-linear regime of structure formation. However, no careful pre-selection of
viable quintessence models with high precision cosmological data was performed.
Here we show that this has led to a misinterpretation (and underestimation) of
the imprint of quintessence on the distribution of large scale structures. To
this purpose we perform a likelihood analysis of the combined Supernova Ia
UNION dataset and WMAP5-years data to identify realistic quintessence models.
Differences from the vanilla LambdaCDM are especially manifest in the predicted
amplitude and shape of the linear matter power spectrum, though these remain
within the uncertainties of the SDSS data. We use these models as benchmark for
studying the clustering properties of dark matter halos by performing a series
of high resolution N-body simulations. We find that realistic quintessence
models allow for relevant differences of the dark matter distribution with the
respect to the LambdaCDM scenario well into the non-linear regime, with
deviations up to 40% in the non-linear power spectrum. Such differences are
shown to depend on the nature of DE, as well as the scale and epoch considered.
At small scales (k~1-5 h Mpc^{-1}, depending on the redshift) the structure
formation process is about 20% more efficient than in LambdaCDM. We show that
these imprints are a specific record of the cosmic structure formation history
in DE cosmologies and therefore cannot be accounted in standard fitting
functions of the non-linear matter power spectrum.
