Cosmographic parameters from current and next-generation gravitational wave detectors

TL;DR

The paper investigates how current and next-generation gravitational-wave detectors can constrain cosmographic parameters using bright sirens with EM counterparts. It employs a third-order Taylor expansion for the luminosity-distance–redshift relation and Bayesian inference on simulated catalogs limited to $z<0.7$, comparing aLIGO, ET, and DECIGO. The results show that aLIGO can deliver a calibration-free measurement of the Hubble constant $H_0$ at a few percent level, while ET and DECIGO achieve sub-percent $H_0$ precision; notably, DECIGO can constrain the deceleration parameter $q_0$ to the percent level and the jerk parameter $j_0$ to tens of percent, enabling tests of dark energy dynamics. The work demonstrates the strong potential of GW standard sirens for low-redshift cosmography, complementing electromagnetic surveys and contributing to efforts to resolve the Hubble tension.

Abstract

We evaluate the capability of current and next-generation gravitational wave detectors, such as Advanced LIGO, Einstein Telescope and DECIGO, to constrain cosmographic parameters using electromagnetically bright standard sirens. By adopting a third-order Taylor expansion, we analyze how signal-to-noise ratios and the number of events impact the estimates of the Hubble constant ($H_0$), the deceleration ($q_0$) and jerk ($j_0$) parameters. Our results show that while Advanced LIGO provides a calibration-free measurement of $H_0$ at the few-percent level, it remains insensitive to higher-order parameters. In contrast, the Einstein Telescope and DECIGO reach sub-percent accuracy for $H_0$. Notably, DECIGO achieves a precision better than 10\% for the deceleration parameter $q_0$ and a few tens of percent for the jerk parameter $j_0$.

Figures (6)

• Figure 1: Luminosity distance as a function of redshift for different orders of the cosmographic series (top panel). The black dashed curve corresponds to the fiducial $\Lambda$CDM model used in the analysis. Relative difference between each cosmographic series and the fiducial model (bottom panel). The gray shaded region indicates a $1\%$ deviation, which is reached by the third-order series at $z \approx 0.7$ (vertical dotted line).
• Figure 2: Normalized redshift probability density function, $P(z)$, for stellar-mass binary systems. The vertical dashed line marks the maximum redshift considered in the analysis, $z_{\rm max} = 0.7$.
• Figure 3: Simulated catalogs of luminosity distance for each interferometer (DECIGO, ET and aLIGO), with the number of detections set to $N_z$ and a maximum redshift of $z_{\mathrm{max}} \simeq 0.7$ (top panel). Fractional uncertainties on the luminosity distance, where the points correspond to the instrumental errors extracted from the simulated catalogs, and the dashed and solid curves represent the systematic contributions from weak lensing and peculiar velocities, respectively, expressed as $\Delta d_L / d_L \times 100\%$ (bottom panel).
• Figure 4: Mean number of simulated events, $\bar{N}$, per signal-to-noise ratio (SNR) interval for each interferometer, averaged over 50 independent realizations. The top-left and top-right panels correspond to aLIGO and the Einstein Telescope, respectively, while the bottom panel shows the results for DECIGO.
• Figure 5: Uncertainties, $\sigma$, of the cosmographic parameters $H_0$, $q_0$, and $j_0$ as functions of the signal-to-noise ratio (SNR). The top, middle, and bottom panels correspond to $H_0$, $q_0$, and $j_0$, respectively. The curves show the results obtained for the different interferometers considered in this analysis.