Large-scale (in) stability analysis of an exactly solved coupled dark-energy model

Abstract

Assuming a nongravitational interaction among the dark fluids of our Universe---namely, dark matter and dark energy---we study a specific interaction model in the background of a spatially flat Friedmann-Lema\^{\i}tre-Robertson-Walker geometry. We find that the interaction model solves the background evolution in an analytic way when the dark energy takes a constant barotropic equation of state, ${w}_{x}$. In particular, we analyze two separate interaction scenarios, namely, when the dark energy is a fluid other than the vacuum energy (i.e., ${w}_{x}\ensuremath{\ne}\ensuremath{-}1$) and when it is vacuum energy itself (i.e., ${w}_{x}=\ensuremath{-}1$). We find that the interacting model with ${w}_{x}\ensuremath{\ne}\ensuremath{-}1$ produces stable perturbations at large scales for ${w}_{x}<\ensuremath{-}1$ with the coupling strength $\ensuremath{\xi}<0$. Both scenarios are constrained by the latest astronomical data. The analyses show that a very small interaction with the coupling strength is allowed, and within the 68.3% confidence region $\ensuremath{\xi}=0$ is recovered. The analyses further show that a large coupling strength significantly affects the large-scale dynamics of the Universe, while according to the observational data the interaction models are very well consistent with $\mathrm{\ensuremath{\Lambda}}$ cosmology. Furthermore, we observe that for the vacuum interaction scenario, the tension on ${H}_{0}$ is not released while for the interacting dark energy scenario with ${w}_{x}<\ensuremath{-}1$, the tension on ${H}_{0}$ seems to be released partially because of the high error bars in ${H}_{0}$. Finally, we conclude the work by calculating the Bayesian evidence, which shows that $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ cosmology is favored over the two interacting scenarios.