Fingerprinting dark energy. III. Distinctive marks of viscosity
The characterization of dark energy is one of the primary goals in cosmology especially now that many new experiments are being planned with the aim of reaching a high sensitivity on cosmological parameters. It is known that if we move away from the simple cosmological constant model then we need to consider perturbations in the dark energy fluid. This means that dark energy has two extra degrees of freedom: the sound speed cs2 and the anisotropic stress σ. If dark energy is inhomogenous at the scales of interest then the gravitational potentials are modified and the evolution of the dark matter perturbations is also directly affected. In this paper we add an anisotropic component to the dark energy perturbations. Following the idea introduced in D. Sapone and M. Kunz, Phys. Rev. D 80, 083519 (2009), we solve analytically the equations of perturbations in the dark sector, finding simple and accurate approximated solutions. We also find that the evolution of the density perturbations is governed by an effective sound speed that depends on both the sound speed and the anisotropic stress parameter. We then use these solutions to look at the impact of the dark energy perturbations on the matter power spectrum and on the integrated Sachs-Wolfe effect in the cosmic microwave background ; D. S. acknowledges support from the JAEDoc program with ref. JAEDoc074 and the Spanish MICINN under the project AYA2009-13936-C06-06. D. S. also acknowledges financial support from the Madrid Regional Government (CAM) under the program HEPHACOS P-ESP-00346, Consolider-Ingenio 2010 PAU (CSD2007-00060), as well as in the European Union Marie Curie Network ''UniverseNet'' under Contract No.MRTNCT- 2006-035863. E.M. was supported by the Spanish MICINNs Juan de la Cierva program (JCI-2010-08112), by CICYT through the project FPA-2009 09017, by the Community of Madrid through the project HEPHACOS (S2009/ESP-1473) under Grant No. P-ESP-00346, and by the European Union ITN project (FP7-PEOPLE-2011-ITN, PITN-GA-2011-289442-INVISIBLES)