Growth index with the exact analytic solution of sub-horizon scale linear perturbation for dark energy models with constant equation of state

Understand

Three decades ago Heath found the integral form of the exact analytic growing mode solution of the linear density perturbation $\delta$ on sub-horizon scales including the cosmological constant or the curvature term.

• Recently, we obtained the exact analytic form of this solution in our previous work \cite{SK}.
• Interestingly, we are able to extend this solution for general dark energy models with the constant equation of state $\omega_{de}$ in a flat universe.
• This analytic solution provides the accurate and efficient tools for probing the properties of dark energy models such as the behavior of the growth factor and the growth index.