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

TL;DR

This paper investigates how different types of couplings between dark energy and dark matter affect the stability of curvature perturbations in cosmological models, revealing conditions for stability based on the nature of the dark energy and the form of coupling.

Contribution

It provides a theoretical analysis of the stability conditions of curvature perturbations in dark sector interaction models, distinguishing effects based on dark energy type and coupling form.

Findings

Coupling proportional to dark matter density causes instability with quintessence dark energy.

Coupling proportional to dark energy density allows stability with quintessence dark energy.

Perturbations remain stable for phantom dark energy regardless of coupling form.

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.