Gravitational wave standard sirens: A brief review of cosmological parameter estimation

TL;DR

GW standard sirens provide direct, calibration-free measurements of luminosity distance via gravitational-wave waveforms, enabling independent constraints on the expansion history and the Hubble constant $H_0$ while offering unique degeneracy-breaking leverage when combined with EM probes. The review categorizes redshift inference into bright, dark, cross-correlation, spectral, and Love-siren approaches within a Bayesian framework, and summarizes current constraints (e.g., GW170817) alongside recent O4a results, which already demonstrate meaningful but still broad uncertainties. Looking ahead, sub-percent $H_0$ precision is anticipated from third-generation ground-based detectors, space-based networks, and PTAs, with complementary power for constraining dark-energy models when leveraging tidal effects, population models, and multi-messenger synergies (FRBs, 21 cm IM, SGL). The work also emphasizes breaking EM degeneracies through joint analyses and the role of machine learning to handle systematics, accelerate inference, and expand the usable event sample. Overall, GW standard sirens are poised to become a central, self-calibrated cosmological probe, particularly when integrated with other late-universe observables.

Abstract

Gravitational wave (GW) observations are expected to serve as a powerful and independent probe of the expansion history of the universe. By providing direct and calibration-free measurements of luminosity distances through waveform analysis, GWs provide a fundamentally different and potentially more robust approach to measuring cosmic-scale distances compared to traditional electromagnetic (EM) observations, which is known as the standard siren method. In this review, we present an overview of recent developments in GW standard siren cosmology, including up-to-date $H_0$ constraints, and prospects for constraining cosmological parameters using future GW detections. A central focus of this review is the unique ability of GW observations to break cosmological parameter degeneracies inherent in the EM observations. We also briefly highlight the impact of systematic uncertainties, such as detector calibration, weak lensing, peculiar velocities, and host-galaxy catalog completeness, and corresponding potential mitigation strategies, which currently limit the constraint precision of cosmological parameters. Looking forward, we highlight the importance of combining GW standard sirens with other emerging late-universe cosmological probes such as fast radio bursts, 21 cm intensity mapping, and strong gravitational lensing to forge a precise cosmological probe for exploring the late universe.

Figures (20)

• Figure 1: Timeline of the discovery of GW170817, GRB 170817A, and SSS17a/AT 2017gfo, along with follow-up observations, shown by messenger and wavelength relative to the GW event time. The figure is from Ref. LIGOScientific:2017ync and reproduced by permission of the AAS.
• Figure 2: Posterior distributions for $H_0$ using the bright siren method from GW170817. The 68.3% ($1\sigma$) and 95.4% ($2\sigma$) minimal credible intervals from GW170817 are indicated by dashed and dotted lines. Constraints on $H_0$ at $1\sigma$ and $2\sigma$ from Planck and distance ladder measurement are shown in green and orange. Reproduced from Ref. LIGOScientific:2017adf with permission.
• Figure 3: Update constraints on the inclination, distance, and $H_0$ from GW170817. Left panel: two-dimensional marginalized posterior contours for the inclination and distance using the Hydro jet (95% confidence level), GW170817 only (68% and 95% confidence level), afterglow light curve (LC) and centroid motion through VLBI (95% confidence level), and their combination with GW170817 assuming power-law jet (PLJ) model (95% confidence level). Right panel: posterior distributions for $H_0$ using GW+VLBI+LC and GW. The $1\sigma$ and $2\sigma$ constraints from Planck CMB and distance ladder are also shown in green and orange vertical bands. Reproduced from Ref. Hotokezaka:2018dfi with permission.
• Figure 4: GW170814 localization, DES galaxy distribution, and the distributions of the DES galaxy redshifts and luminosity distance in the localization region. Left panel: the GW170814 localization region at 50% and 90% confidence level and the used stellar mass distribution of DES galaxies. The galaxy's stellar mass distribution in RA and redshift, projected over DEC. Right panel: the distributions of the DES galaxy redshifts within the region of interest and the luminosity distance in HEALPIX pixels from the distance likelihood. The figure is from Ref. DES:2019ccw and reproduced by permission of the AAS.
• Figure 5: The posterior distributions for $H_0$ using the DES GW170814 dark siren, GW170817 bright siren, SH0ES distance ladder, and Planck CMB observation. The figure is from Ref. DES:2019ccw and reproduced by permission of the AAS.