# Prospect for constraining holographic dark energy with gravitational wave standard sirens from the Einstein Telescope

## TL;DR

This paper explores how future gravitational wave observations from the Einstein Telescope can significantly improve constraints on holographic dark energy models, especially when combined with other cosmological data.

## Contribution

It demonstrates that GW standard siren data can greatly enhance the precision of cosmological parameter estimation in holographic dark energy models.

## Key findings

- GW data improves parameter constraints by over 70%
- Combined data measures $
m \Omega_m$, H_0, and c with high accuracy
- GW data alone provides good $H_0$ estimates but weak for others

## Abstract

We study the holographic dark energy (HDE) model by using the future gravitational wave (GW) standard siren data observed from the Einstein Telescope (ET) in this work. We simulate 1000 GW standard siren data based on a 10-year observation of the ET to make this analysis. We find that all the cosmological parameters in the HDE model can be tremendously improved by including the GW standard siren data in the cosmological fit. The GW data combined with the current cosmic microwave background anisotropies, baryon acoustic oscillations, and type Ia supernovae data will measure the cosmological parameters $\Omega_{\rm m}$, $H_0$, and $c$ in the HDE model to be at the accuracies of 1.28%, 0.59%, and 3.69%, respectively. A comparison with the cosmological constant model and the constant-$w$ dark energy model shows that, compared to the standard model, the parameter degeneracies will be broken more thoroughly in a dynamical dark energy model. We find that the GW data alone can provide a fairly good measurement for $H_0$, but for other cosmological parameters the GW data alone can only provide rather weak measurements. However, due to the fact that the parameter degeneracies can be broken by the GW data, the standard sirens can play an essential role in improving the parameter estimation.