Dark sector evolution in Horndeski models

Understand

We use the Equation of State (EoS) approach to study the evolution of the dark sector in Horndeski models, the most general scalar-tensor theories with second order equations of motion.

• By including the effects of the dark sector into our code EoS\_class, we demonstrate the numerical stability of the formalism and excellent agreement with results from other publicly available codes for a range of parameters describing the evolution of the function characterising the perturbations for Horndeski models, $\alpha_{\rm x}$, with ${\rm x}=\{{\rm K}, {\rm B}, {\rm M}, {\rm T}\}$.
• After demonstrating that on sub-horizon scales ($k\gtrsim 10^{-3}~{\rm Mpc}^{-1}$ at $z=0$) velocity perturbations in both the matter and the dark sector are typically subdominant with respect to density perturbations in the equation of state for perturbations, we find an attractor solution for the dark sector gauge-invariant density perturbation $\Delta_{\rm ds}$ by neglecting its time derivatives in the equation describing its time evolution, as commonly done in the well-known quasi-static approximation.
• Using this result, we provide simplified expressions for the equation-of-state functions: the dark sector entropy perturbations $w_{\rm ds}\Gamma_{\rm ds}$ and anisotropic stress $w_{\rm ds}\Pi_{\rm ds}$.