Stability of the curvature perturbation in dark sectors' mutual interacting models

Abstract

We consider perturbations in a cosmological model with a small coupling between dark energy and dark matter. We prove that the stability of the curvature perturbation depends on the type of coupling between dark sectors. When the dark energy is of quintessence type, if the coupling is proportional to the dark matter energy density, it will drive the instability in the curvature perturbations; however if the coupling is proportional to the energy density of dark energy, there is room for the stability in the curvature perturbations. When the dark energy is of phantom type, the perturbations are always stable, no matter whether the coupling is proportional to the one or the other energy density.

Figures (4)

• Figure 1: The upper two figures show the scaling behavior of $\lambda_1 r$. The lower two show the behavior of the perturbation.
• Figure 2: Comparisons of $\xi_1$ and $\xi_2$.
• Figure 3: Behavior of the indices $r_1$ and $r_2$ in terms of $w$.
• Figure 4: Behavior of $\Delta$ and of $\Gamma$.