Combined constraints on deviations of dark energy from an ideal fluid from Euclid and Planck

Cosmological fluids are commonly assumed to be distributed in a spatially homogeneous way, while their internal properties are described by a perfect fluid. As such, they influence the Hubble expansion through their respective densities and equation-of-state parameters. The subject of this paper is an investigation of the fluid-mechanical properties of a dark energy fluid, which is characterized by its sound speed and its viscosity apart from its equation of state. In particular, we compute the predicted spectra for the integrated Sachs-Wolfe effect for our generalized fluid, and compare them with the corresponding predictions for weak gravitational lensing and galaxy clustering, which had been computed in previous work. We perform statistical forecasts and show that the integrated Sachs-Wolfe signal obtained by cross-correlating Euclid galaxies with Planck temperatures, when joined to galaxy clustering and weak lensing observations, yields a percent sensitivity on the dark energy sound speed and viscosity. We prove that the iSW effect provides strong degeneracy breaking for low sound speeds and large differences between the sound speed and viscosity parameters.