Constraining Dark Energy Anisotropic Stress

TL;DR

<3-5 sentence high-level summary> Addresses whether dark energy can exhibit anisotropic stress and how to constrain it with cosmological data. It introduces a general fluid parameterization including the equation of state $w$, the rest-frame sound speed $c^2_{lam}$, and anisotropic-stress parameters $c^2_{vis}$ and $\alpha_{vis}$, and analyzes CMB, LSS, and SNIa data with CosmoMC. The results show that present data yield weak constraints on these perturbation parameters and that even a cosmic-variance-limited future CMB would offer limited improvement, suggesting a perfect-fluid (with $\Sigma_{\mu\nu}=0$) description may be observationally adequate. Nevertheless, the authors emphasize that observational data cannot completely rule out imperfectness in dark energy.

Abstract

We investigate the possibility of using cosmological observations to probe and constrain an imperfect dark energy fluid. We consider a general parameterization of the dark energy component accounting for an equation of state, speed of sound and viscosity. We use present and future data from the cosmic microwave background radiation (CMB), large scale structures and supernovae type Ia. We find that both the speed of sound and viscosity parameters are difficult to nail down with the present cosmological data. Also, we argue that it will be hard to improve the constraints significantly with future CMB data sets. The implication is that a perfect fluid description might ultimately turn out to be a phenomenologically sufficient description of all the observational consequences of dark energy. The fundamental lesson is however that even then one cannot exclude, by appealing to observational evidence alone, the possibility of imperfectness in dark energy.

Figures (12)

• Figure 1: The CMB temperature power spectrum for models with different values of $w$ and $c^2_{vis}$. The upper panel is for a model with $w=-1.2$ and $c^2_{vis} \leq 0$, while the lower panel shows the results for a model with $w=-0.8$ and $c^2_{vis} \geq 0$. The grey shading indicates the cosmic variance around the models with $c^2_{vis} = 0$. All models plotted here have $c^2_{lam}=1$.
• Figure 2: The CMB temperature power spectrum for models with different values of $w$ and $c^2_{lam}$. The upper panel shows the results for a model with $w=-1.2$, while the lower panel shows models with $w=-0.8$. The grey shading indicates the cosmic variance. All models shown here $c^2_{vis}=0$.
• Figure 3: 68% and 95% contours of $c^2_{vis}$ and $w$. In the upper panel $w>-1$ and $c^2_{vis}>0$, while in the lower panel $w<-1$ and $c^2_{vis}<0$. We see that the constraints are much tighter for negative $c^2_{vis}$ than for positive. In the right plot we have also shown how the constraints improve when including SDSS-LRG and SNLS data (dotted black contours). In these models $c^2_{lam}=1$.
• Figure 4: 68% and 95% contours of $\alpha_{vis}$ and $w$. We see that slightly negative values of $\alpha_{vis}$ are allowed, and that the allowed values for $\alpha_{vis}$ in this parameter range has only a weak dependence on $w$. In this model $c^2_{lam}=1$.
• Figure 5: Marginalized probability distribution for $\log(\alpha_{vis})$ for a model with $w=-1.2$ and $c^2_{lam}=1$.