Illuminating Dark Energy with Bright Standard Sirens from Future Detectors

Abstract: Understanding the nature and evolution of dark energy (DE) is a central challenge in modern cosmology. In this work, we explore the constraining power of bright standard sirens -- gravitational wave (GW) events with electromagnetic counterparts - for probing the DE equation of state as function of redshift. Focusing on future GW observations from next-generation ground-based GW detectors such as the Einstein Telescope and Cosmic Explorer, we perform a comprehensive analysis using simulated binary neutron star (BNS) and neutron star-black hole (NSBH) events over five years of observation with a $75\%$ duty cycle. We consider three broad classes of DE models: (i) phenomenological parametrizations, specifically the Barboza-Alcaniz extension to the Chevallier-Polarski-Linder model; (ii) physically motivated scalar field scenarios, specifically hilltop quintessence; and (iii) evolving dark matter setup in which the matter density evolves as $(1+z)^{3+\alpha}$. For each case, we jointly infer the Hubble constant $H_0$ and model-specific DE parameters from the observed GW luminosity distances and spectroscopic redshifts. Our results demonstrate that bright sirens alone can yield competitive and independent constraints on the time evolution of DE indicating that multi-messenger cosmology has the potential to test a wide range of DE theories, bridging phenomenological and physically motivated models, and paving the way for precision cosmology in the era of GW astronomy.