Matter sourced anisotropic stress for dark energy

Usually a dark energy as a perfect fluid is characterized by the ratio of pressure to energy density (w = p/rho) and the ratio of their perturbations in its rest frame (c(s)(2) = delta p/delta rho). However, a dark energy would have other characteristics beyond its equation of state and the effective speed of sound. Here the extra property is the anisotropic stress sourced by matter as a simple extension to the perfect fluid model. At the background level, this anisotropic stress is zero with respect to the cosmological principle, but not at the first-order perturbation. We tested the viability of the existence of this kind of anisotropic stress by using the currently available cosmic observations through the geometrical and dynamical measurements. Using the Markov-chain Monte Carlo method, we found that the upper bounds on the anisotropic stress which enters into the summation of the Newtonian potentials should be of the order O(10(-3))Delta(m). We did not find any strong evidence for the existence of this matter-sourced anisotropic stress, even in the 1 sigma region.