Dark Energy Anisotropic Stress and Large Scale Structure Formation

TL;DR

The paper investigates whether an imperfect dark energy component with anisotropic stress can leave detectable signatures in large-scale structure and the CMB. It introduces a phenomenological three-parameter fluid with equation of state $w$, sound speed $c_s^2$, and viscosity parameter $c_{vis}^2$, and derives perturbation equations in the synchronous gauge, including a dynamical equation for the anisotropic stress $\sigma$. Across constant-parameter scenarios, it shows that anisotropic stress can amplify or suppress the ISW effect depending on the sign of $w$, and that degeneracies with $c_s^2$ can mask these signatures; negative $c_s^2$ can be viable when shear is present, potentially explaining a low CMB quadrupole. The analysis extends to imperfect unified models like Chaplygin gas and the modified polytropic Cardassian expansion, where shear can stabilize density perturbations and modestly improve compatibility with large-scale structure, though CMB ISW constraints remain strong. Overall, dark energy anisotropic stress is not ruled out by current data, and future cross-correlations between ISW, galaxy surveys, and lensing could tighten constraints on this degrees of freedom and the time evolution of $w$, $c_s^2$, and $c_{vis}^2$.

Abstract

We investigate the consequences of an imperfect dark energy component on the large scale structure. A phenomenological three parameter fluid description is used to study the effect of dark energy on the cosmic microwave background radiation (CMBR) and matter power spectrum. In addition to the equation of state and the sound speed, we allow a nonzero viscosity parameter for the fluid. Then anisotropic stress perturbations are generated in dark energy. In general, we find that this possibility is not excluded by the present day cosmological observations. In the simplest case when all of the three parameters are constant, we find that the observable effects of the anisotropic stress can be closely mimicked by varying the sound speed of perfect dark energy. However, now also negative values for the sound speed, as expected for adiabatic fluid model, are tolerable and in fact could explain the observed low quadrupole in the CMBR spectrum. We investigate also structure formation of imperfect fluid dark energy characterized by an evolving equation of state. In particular, we study unified models of dark energy with dark matter, such as the Chaplygin gas or the Cardassian expansion, with a shear perturbation included. This can stabilize the growth of inhomogeneities in these models, thus somewhat improving their compatibility with large scale structure observations.

Figures (11)

• Figure 1: Late evolution of the dark energy density perturbation and velocity potential for $k=1.3\cdot 10^{-4}$ Mpc$^{-1}$ when $w=-0.8$. Solid lines from top to bottom correspond to $\delta$, and dashed lines from bottom to top correspond to $(1+w)H\theta/k^2$ when ($c_{s}^2$, $c_{vis}^2$) = (0,0), (0.6,0), (0,0.6), (0.6,0.6). The effect of $c_{vis}^2$ is to damp density perturbations, which in the synchronous gauge is seen as a consequence of enhancing the velocity perturbations.
• Figure 2: Late evolution of the gravitational potentials at large scales ($k=1.3\cdot 10^{-4}$ Mpc$^{-1}$) when $w=-0.8$ and $c_s^2=0$. Solid lines are for the case of perfect dark energy and dashed for the imperfect case with $c_{vis}^2=1.0$ The upper lines are $\psi$, the lower lines are $\phi$.
• Figure 3: The CMBR anisotropies for $w=-0.8$. In the upper panel $c_s^2=0$ and in the lower panel $c_s^2=1.0$. The ISW contribution increases with the parameter $c^2_{vis}$: thick lines are for $c^2_{vis}=0$, dash-dotted for $c^2_{vis}=0.001$, dashed for $c^2_{vis}=0.01$, dotted for $c^2_{vis}=0.1$ and the solid lines for $c^2_{vis}=1.0$.
• Figure 4: Late evolution of the dark energy density perturbation and and the velocity potential for $k=1.3 \cdot 10^{-4}$ Mpc$^{-1}$ when $w=-1.2$. Solid lines from bottom to top correspond to $\delta$, the dashed lines from top to bottom correspond to $(1+w)H\theta/k^2$ when ($c_s^2$, $c_{vis}^2$) = (0,0), (0.6,0), (0,-0.6), (0.6,-0.6). The effect of $c_{vis}^2$ is to increase clustering, which in the synchronous gauge is seen as a consequence of enhancing the velocity perturbations.
• Figure 5: Late evolution of the gravitational potentials at large scales( $k=1.3\cdot 10^{-4}$ Mpc$^{-1}$) when $w=-1.2$ and $c_s^2=0$. Solid lines are for the case of perfect dark energy and, dashed for the imperfect case with $c_{vis}^2=-1.0$. The upper lines are $\phi$, the lower lines are $\psi$.