Can dark energy viscosity be detected with the Euclid survey?
  Recent work has demonstrated that it is important to constrain the dynamics
of cosmological perturbations, in addition to the evolution of the background,
if we want to distinguish among different models of the dark sector. Especially
the anisotropic stress of the (possibly effective) dark energy fluid has been
shown to be an important discriminator between modified gravity and dark energy
models. In this paper we use approximate analytical solutions of the
perturbation equations in the presence of viscosity to study how the
anisotropic stress affects the weak lensing and galaxy power spectrum. We then
forecast how sensitive the photometric and spectroscopic Euclid surveys will be
to both the speed of sound and the viscosity of our effective dark energy fluid
when using weak lensing tomography and the galaxy power spectrum. We find that
Euclid alone can only constrain models with very small speed of sound and
viscosity, while it will need the help of other observables in order to give
interesting constraints on models with a sound speed close to one. This
conclusion is also supported by the expected Bayes factor between models.
