# Forecasting the Interaction in Dark Matter-Dark Energy Models with Standard Sirens From the Einstein Telescope

## TL;DR

This paper explores how future gravitational wave observations from the Einstein Telescope can improve constraints on interacting dark matter-dark energy models by simulating standard siren data and performing statistical analysis.

## Contribution

It introduces a method to use simulated GW+GRB events from the Einstein Telescope to constrain dark sector interaction parameters, enhancing current cosmological constraints.

## Key findings

- GW observations can significantly improve constraints on DM-DE interaction.
- Simulated data shows potential for tighter bounds on model parameters.
- Future detectors like Einstein Telescope will be crucial for dark energy research.

## Abstract

Gravitational Waves (GW's) can determine the luminosity distance of the progenitor directly from the amplitude of the wave, without assuming any specific cosmological model. Thus, it can be considered as a standard siren. The coalescence of binary neutron stars (BNS) or neutron star-black hole pair (NSBH) can generate GW's as well as the electromagnetic counterpart, which can be detected in a form of Gamma-Ray Bursts (GRB) and can be used to determine the redshift of the source. Consequently, such a standard siren can be a very useful probe to constrain the cosmological parameters. In this work, we consider an interacting Dark Matter-Dark Energy (DM-DE) model. Assuming some fiducial values for the parameters of our model, we simulate the luminosity distance for a "realistic" and "optimistic" GW+GRB events , which can be detected by the third-generation GW detector Einstein Telescope (ET). Using these simulated events, we perform a Monte Carlo Markov Chain (MCMC) to constrain the DM-DE coupling constant and other model parameters in $1\sigma$ and $2\sigma$ confidence levels. We also investigate how GW's can improve the constraints obtained by current cosmological probes.