Fingerprinting Dark Energy III: distinctive marks of viscosity

TL;DR

This paper explores how dark energy perturbations, including anisotropic stress, influence cosmic structures and the CMB, providing analytical solutions that help distinguish dark energy models with viscosity.

Contribution

It introduces an analytical framework for dark energy perturbations with anisotropic stress, extending previous models to include viscosity effects.

Findings

Effective sound speed depends on sound speed and anisotropic stress

Dark energy perturbations impact matter power spectrum

Alterations in the Integrated Sachs-Wolfe effect are identified

Abstract

The characterisation 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 $\cs$ and the anisotropic stress $\sigma$. 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 \cite{Sapone:2009mb}, 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 which 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.