Exact analytic solution of sub-horizon scales linear perturbation for
  general dark energy models
  Three decades ago Heath found the integral form of the exact analytic growing
mode solution of linear density perturbation $\delta$ in sub-horizon scales
including the cosmological constant or the curvature term. Interestingly, we
are able to obtain the analytic solution for general dark energy models with
the constant equation of state $\omega_{de}$. We compare the correct analytic
growing mode solution $\delta$ with the text book solution $\delta^{D}$.
Indeed, both solutions are equal to each other when $\omega_{de} = -1$. We also
able to extend this solution for the specific form of time varying
$\omega_{de}$.
