# Large-scale Stability and Astronomical Constraints for Coupled Dark-Energy Models

## TL;DR

This paper investigates large-scale inhomogeneous perturbations in interacting dark energy models, proposing a modification to test the entire parameter space against observational data, and finds small deviations from the standard cosmological model.

## Contribution

The study introduces a factor $(1+w_x)$ in the energy transfer, enabling comprehensive testing of IDE models and removing previous instabilities, with constraints derived from latest astronomical data.

## Key findings

- Small non-zero interaction coupling strengths are favored.
- Dark energy EoS tends towards the phantom region but allows $w_x > -1$.
- Behavior shifts from phantom to quintessence as Hubble constant decreases.

## Abstract

We study large-scale inhomogeneous perturbations and instabilities of interacting dark energy (IDE) models. Past analysis of large-scale perturbative instabilities, has shown that we can only test IDE models with observational data when its parameter ranges are either $w_{x}\geq -1$ and $\xi \geq 0,$ or $w_{x}\leq -1~$ and $~\xi \leq 0$, where $w_{x}$ is the dark energy equation of state (EoS), and $\xi$ is a coupling parameter governing the strength and direction of the energy transfer. We show that by adding a factor $(1+w_{x})$ to the background energy transfer, the whole parameter space can be tested against all the data and thus, the instabilities in such interaction models can be removed. We test three classes of interaction model using the latest astronomical data from different sources. Precise constraints are found. Our analysis shows that a very small but non-zero deviation from pure $\Lambda$-cosmology is suggested by the observational data while the no-interaction scenario can be recovered at the 68.3% confidence-level. In particular, for three IDE models, identified as IDE 1, IDE 2, and IDE 3, the 68.3% CL constraints on the interaction coupling strengths are, $\xi= 0.0360_{-0.0360}^{+0.0091}$ (IDE 1), $\xi= 0.0433_{-0.0433}^{+0.0062}$ (IDE 2), $\xi= 0.1064_{-0.1064}^{+0.0437}$ (IDE 3). In addition, we find that the dark energy EoS tends towards the phantom region taking the 68.3% CL constraints, $w_x= -1.0230_{-0.0257}^{+0.0329}$ (IDE 1), $w_x= -1.0247_{-0.0302}^{+0.0289}$ (IDE 2), and $w_x= -1.0275_{-0.0318}^{+0.0228}$ (IDE 3). However, the possibility of $w_{x}>-1$ is also not rejected by the astronomical data used here. Moreover, we find in all IDE models that, as the value of Hubble constant decreases, the behavior of the dark energy EoS shifts from phantom to quintessence type with its EoS very close to that a simple cosmological constant at the present time.