Fingerprinting Dark Energy II: weak lensing and galaxy clustering tests
  The characterization of dark energy is a central task of cosmology. To go
beyond a cosmological constant, we need to introduce at least an equation of
state and a sound speed and consider observational tests that involve
perturbations. If dark energy is not completely homogeneous on observable
scales then the Poisson equation is modified and dark matter clustering is
directly affected. One can then search for observational effects of dark energy
clustering using dark matter as a probe. In this paper we exploit an analytical
approximate solution of the perturbation equations in a general dark energy
cosmology to analyze the performance of next-decade large scale surveys in
constraining equation of state and sound speed. We find that tomographic weak
lensing and galaxy redshift surveys can constrain the sound speed of the dark
energy only if the latter is small, of the order of $c_{s}\lesssim0.01$ (in
units of $c$). For larger sound speeds the error grows to 100% and more. We
conclude that large scale structure observations contain very little
information about the perturbations in canonical scalar field models with a
sound speed of unity. Nevertheless, they are able to detect the presence of
"cold" dark energy, i.e. a dark energy with non-relativistic speed of sound.
