# Quantifying the impacts of future gravitational-wave data on constraining interacting dark energy

## TL;DR

This study assesses how future gravitational-wave observations from the Einstein Telescope could enhance constraints on interacting dark energy models by combining simulated GW data with existing electromagnetic observations.

## Contribution

It introduces a method to incorporate simulated GW data into cosmological parameter estimation for interacting dark energy models, improving constraint accuracy.

## Key findings

- GW data significantly improves constraints on H0, w, and Omega_m.
- Adding GW data slightly refines the coupling parameter beta.
- The approach avoids large-scale instability issues in IDE models.

## Abstract

In this work, we investigate the impacts of the future gravitational-wave (GW) standard siren observation by the Einstein Telescope (ET) on constraining the interacting dark energy (IDE) models. We simulate 1000 GW events in the redshift range of $0\lesssim z \lesssim 5$ based on the 10-year observation of the ET. We combine the simulated GW data with the current mainstream cosmological electromagnetic observations including the cosmic microwave background anisotropies, the baryon acoustic oscillations, and the type Ia supernovae to constrain the IDE models. We consider typical IDE models in the context of a perturbed universe. To avoid the large-scale instability problem for IDE models, we apply the extended parameterized post-Friedmann approach to calculate the cosmological perturbations. We find that the addition of the GW standard siren data could significantly improve the constraint accuracies for most of the cosmological parameters (e.g., $H_{0}$, $w$, and $\Omega_{\rm m}$). For the coupling parameter $\beta$, the constraint errors could also be slightly improved when adding the GW data in the cosmological fit.